Mech.  ri«ot. 


Engineering 
Library 


CONTINUOUS    CURRENT   MACHINE 
DESIGN 


CONTINUOUS    CURRENT 
MACHINE    DESIGN 


BY 


WILLIAM    CRAMP,    M.SC.TECH.,    M.I.E.E. 

CONSULTING    ENGINEER,    SPECIAL    LECTURER    IN    ELECTRICAL    DESIGN,    THE  VICTORIA    UNIVERSITY 

MANCHESTER,    SOMETIME    LECTURER    IN    ELECTRO-TECHNOLOGY    AT    THE 

CENTRAL    TECHNICAL    COLLEGE,    LONDON 


LONDON   AND   NEW   YORK 

HARPER    6f   BROTHERS 

45,   ALBEMARLE    STREET,  W. 
1910 

(All  rights  reserved) 

D.  VAN  NOSTRAND  COMPANY 

NEW   YORK 


T  k 

017 


ibrary 


TO  THE  MEMORY 

OF 

MY   FRIEND   AND   UNCLE 

THOMAS   WILLIAM   KOBINSON 


410350 


PREFACE 

IN  attempting  to  find  at  a  reasonable  price,  and  between  one  pair  of 
covers,  a  text-book  for  the  more  advanced  student  of  Continuous 
Current  Machine  Design,  I  have  met  with  perpetual  difficulty.  It 
seems  to  me  that  the  text-books  hitherto  published  fall  naturally 
into  two  groups — those  which  cost  too  much,  and  those  which  are 
too  special.  The  former  have  grown  up  with  the  subject,  and  in 
process  of  time  successive  editions  and  additions  have  brought  them 
to  a  state  reminding  one  of  the  fifth  age  of  man.  To  these  standard 
works  all  students  are  indebted ;  though  few  can  afford  to  buy  them : 
they  are  indeed  often  regarded  as  luxuries  to  be  found  in  reference 
libraries  only.  Books  of  the  second  class  are  usually  written  to 
cover  special  ground  at  a  special  time,  to  act  as  vade  mecum  to  a 
particular  examination,  or  to  render  temporary  assistance  to  the 
expert. 

In  the  present  volume  I  have  tried  to  avoid  these  extremes  by 
omitting  all  that  a  student  may  reasonably  be  expected  to  know 
at  the  end  of  his  second  year,  and  by  indicating  the  road  along 
which  designers  have  hitherto  travelled  and  the  direction  in  which 
the  next  move  is  likely  to  be  made.  It  is  my  hope  that  the  book 
may  be  a  useful  companion  to  the  student,  both  in  the  drawing 
office  and  in  the  class-room,  as  well  as  a  stimulating  and  sug- 
gestive guide  to  the  teacher.  In  recent  design  the  introduction  of  the 
"  commutating  pole  "  or  "  interpole  "  has  been  responsible  for  a  great 
many  changes ;  and  these  account  for  the  large  proportion  of  this 
volume  devoted  to  temperature  rise.  Yet,  lest  a  change  in  the  price 
of  copper  should  some  day  abolish  the  interpoles,  machines  not 
dependent  upon  them  are  also  fully  considered. 

Both  in  the  text  and  in  the  Examples  of  Procedure  I  have  tried 
to  lay  stress  upon  the  tentative  and  experimental  nature  of  the 


viii  PREFACE 

subject,  as  also  upon  the  number  of  variables  involved,  the  ever- 
present  influence  of  cost,  and  the  careful  comparisons  that  should 
be  carried  out  before  any  design  is  adopted.  Further,  that  the  text 
might  not  be  unduly  encumbered,  those  pages  which  would  otherwise 
look  like  excerpts  from  an  algebra  have  been  relegated  to  an  appendix. 
Throughout  the  calculated  examples  little  or  no  attempt  has  been 
made  to  carry  accuracy  further  than  four  significant  figures.  This 
is,  I  think,  rational ;  for  the  practised  designer  will  be  the  first  to 
admit  that  the  available  data  rarely  allow  of  a  closer  approximation. 

It  remains  for  me  to  acknowledge  the  substantial  assistance  I 
have  received  from  Mr.  J.  Lustgarten,  M.Sc.,  in  Chapters  VI.,  VII. , 
and  VIII.,  and  from  Mr.  Thomas  Jones  in  the  diagrams  of  Chapter 
XI.  To  Professor  Marcus  Hartog,  who  carefully  read  the  proofs, 
I  am  also  much  indebted,  as  well  as  to  the  various  manufacturers 
who  have  kindly  lent  me  blocks. 

I  dare  not  hope  that  a  book  compiled  in  the  spare  moments  of 
over-full  days  can  have  escaped  without  some  mistakes ;  if  any  reader 
will  bring  such  errors  to  my  notice  I  shall  be  very  grateful. 

WILLIAM   CRAMP. 
20,  MOUNT  ST.,  MANCHESTER, 
August,  1910. 


TABLE    OF    CONTENTS 

i 

CHAPTER  I 

THE  FORM  OF  MODERN  MACHINES 

PAGE 

Introduction — General  Forms         .........  1 

Present  Practice — Form  of  Field  Magnets — Cast  Iron— Cast  Steel  and  Wrought 

Iron        .............  2 

Cast  Steel— Malleable  Iron— Field  Poles         .......  5 

Machines  without  Pole-tips— Ordinary  Forms  of  Field-construction          .         .  6 

Laminated  Poles— Comparison  of  Circular  and  Eectangular  Pole — Circular  Pole  7 

Square  Pole  .............  8 

Other  Types  of  Field-magnet .         .         . 9 

Multipolar  and  Bipolar  Machines 10 

General  Form  of  Armatures — General  Form  of  Commutators  ....  11 

CHAPTER  II 

GENERAL  PROPORTIONS  OF  MODERN  MACHINES 

Limiting  Densities :  (1)  Yoke ;  (2)  Pole ;  (3)  Air-gap— Air-gap  Length  .         .       13 
Eelative  Constancy  of  the  Field  Ampere-turns — The  Ratio  Pole-arc :  Pole-pitch       14 

Armature-teeth— Number  of  Teeth          .         .         .                ;  .        .'  15 

Dimensions  of  the  Armature  below  the  Teeth  ....  16 

Relationship  between  Field  and  Armature  Dimensions    .         .    .  19 

General  Relationship  between  Output  and  Dimensions    .  21 

Armature  Peripheral  Speed— Commutator  Peripheral  Speed    .  24 

CHAPTER  III 
RELATIVE  PROPORTIONS  OF  THE  ARMATURE  PARTS 

1.  Efficiency,  and  2,  Division  of  Losses  for  a  given  Temperature-rise — 3.  Pres- 
sure and  Current — 4.  Standardization — 5.  Appearance — 6.  Ampere-turns 
of  the  armature— 7.  Commutation — 8.  Use  of  Neutralization — (I.)  Efficiency 
Characteristic  required — (a)  Constant  Losses,  (&)  Variable  Losses  .  25 


Allotment  of  Constant  Losses 

Estimation  of  Iron  Loss 

Variable  Losses 

(II.)  Effect  of  Enclosing 

Estimation  of  Copper  Loss— 3.  Influence  of  Pressure  and  Current 


28 
29 
30 
31 
32 


4.  Standardization 33 

Appearance — 6.  Ampere-turns  of  the  Armature— 7.  Commutation — 8.  Use  of 

Neutralization         .         .         .         .         .  Y        .         .      ^  .         •       34 

a2 


TABLE   OF   CONTENTS 


CHAPTER  IV 

RELATIVE  PROPORTIONS  OF  THE  FIELD  MAGNET  PARTS- 
FIELD  CALCULATION 

PAGE 

Corrections  to  the  above  Calculation — I.  Effective  Area  of  Gap        ...      39 

Example  of  Corrected  Pole-arc— Effect  of  Slots 40 

Correction    of    Tooth-density — Ampere-turns    for  High     Tooth-densities— II. 

Leakage  Factor       .         .         . 42 

Value  of  Leakage  Factor 44 

Example  of  Approximate  Leakage  Factor  Calculation       .....       45 

Leakage  Flux  at  the  Mouth  of  a  Slot ;        .         .         .47 

Magnetization  Curve      .        V        .         .         .         .         .         .         .         .         .48 

Interpole  Calculation .49 


CHAPTER  V 

RELATIONSHIP   BETWEEN  ARMATURE   AND  FIELD   STRENGTH- 
FIELD   CALCULATION 

Armature  Reaction .50 

Field  Diagram  with  Brushes  moved  forward  to  the  Neutral  Position — To  show 

that  the  Brushes  may  be  obtained  in  the  Actual  Neutral  Position  .  .  52 

Besultant  Field 53 

Back  AT  in  Multipolar  Machines — Use  of  Neutralization  ....  54 

To  calculate  the  Total  AT  for  the  Field  .  .  ." 55 

Field  Coil  Calculations 56 

Shunt  Coil  Calculations— Allowances  for  Insulation  on  the  Wire  ...  57 
Arrangement  of  Series  and  Shunt  Coils — Construction  of  Compound  Coils — 

Example  of  Preliminary  Calculation  of  a  Compound  Winding  ...  58 

Compound  Winding— Back  Ampere-turns 59 

The  Limit  of  Output  imposed  by  Armature  Reaction  .....  60 

Armature  Reaction  in  Neutralized  Machines  .  .  .  61 


CHAPTER  VI 

TEMPERATURE  RISE— FIELD  COILS 

Causes  of  Heat * .         .63 

Cooling  Factors — Laws  connecting  Heating  and  Cooling  ....       64 

Final  Temperature — Intermittent  Loading      .         .         .         .         .         .         .65 

Rating  for  Continuous  Working — Rating  for  Intermittent  Working  .         .       66 

Heating  of  Coils 67 

Limiting  Temperatures  for  Coverings— Temperature-rise  Standards          .         .      69 

Heating 70 

Deductions  from  the  Results .         .         .       '-....         ..      .         .        "•         •       73 

General  Formulae .         .74 

Example 75 

Calculation  of  Ventilated  Coil.     Shunt  Winding — Series-winding — Size  of  wire       77 
Notes  on  the  above  Calculations— Cost  of  Ventilated  Coils       .         .  .78 


TABLE   OF   CONTENTS 


XI 


CHAPTER  VII 

TEMPERATURE  RISE— ARMATURES  AND   COMMUTATORS 

PAGK 

Heating  of  Armatures    .         .         .         .         .         .         .         .  .         .79 

Measurement  of  Armature  Temperature — Methods  of  estimating  Temperature- 
rise         .  ,  80 


Comparison  of  Methods  .... 

General  Dimensions  derived  from  Heating  Formulae 

Commutators 

Heating  of  Totally  Enclosed  Motors 


84 
85 
86 
87 


CHAPTER  VIII 

ARMATURE   WINDINGS 

Types  of  Armature  Winding— Closed  Coil  Armatures                         .         .         .  89 

Elementary  Bi-polar  Ring— Turns  per  Segment       .                           ...  90 

Multipolar  Simple  Ring- winding — Pitch  .  .        '.         .91 

Commutator  Pitch — Drum  Windings     .         .         .  .         .         .92 

Progressive  and  Retrogressive  Windings                   .                           ...  93 

Multipolar  Drum  Windings .         *.         .  94 

Conventional  Winding  Table  ...                  .                           ...  95 

Development — Chord  Winding — Resistance  of  Drum  Winding          ...  96 

Duplex  Multiple-circuit  or  Lap  Windings— Object  of  a  Double  Winding  .         .  97 
Multiplex    Multiple-circuit    Windings    (Multiple    Re-entrancy) :    Notation — 

Multiplex  Drum  Windings  of  Multiple  Re-entrancy 98 

Pitch  of  Multiplex  Lap  Windings  of  Multiple  Re-entrancy            •  *  .    •               .  99 

Circuits  through  the  Winding— Duplex  Winding  Singly  Re-entrant           .         .  100 

Notation  to  express  these  Windings — Quadruple  Winding  Double  Re-entrant  .  101 

The  Duplex  Drum  Singly  Re-entrant 102 

Re-entrancy  of  Lap  Windings — Summary  of  Rules  for  Multiple-circuit  Drum 

Windings 103 

Equalizing  Rings  .         .         .         .         ......         .         .         .  104 

Two-circuit  or  Wave  Windings       .         .         .         .         .         ,         .         .         .105 

Circuits  and  Brushes  in  Two-circuit  Windings         ......  106 

Resistance  of  a  Two-circuit  Winding — Formula  for  Two-circuit  Winding .         .  107 
Creep — Progressive  and    Retrogressive    Wave   Winding — Forward  and   Back 

Pitches 108 

Commutator  Pitch  of  Two-circuit  Windings — Multiplex  Wave  Windings — Im- 
portance of  Multiplex  Two-circuit  Drum  Windings— Rules  governing  Two- 
circuit  Windings  .  .  .  . 109 

Coil  and  Slot  Windings— Coil  Windings 110 

Grouping  of  Conductors  in  Slots — Meaning  of  Slot  Winding-pitch  111 

Grouping  of  Coils  in  Slots .  112 

Idle  or  Dummy  Coils — Best  Numbers  of  Slots  for  Two-circuit  Windings — 

Comparison  of  Lap  and  Wave  Windings   ....  115 

The  Same  Armature  as  Wave  Wound  and  Lap  Wound     .  116 


xii  TABLE   OF   CONTENTS 

CHAPTER    IX 

COMMUTATION 

PAGE 

Consideration  of  Commutation  in  Ring  Armatures  .         .         ...         .117 

Commutation  in  Drum  Armatures — Methods  of  Commutation.  .  .  .  119 

E.M.F.  Commutation .  .  .  120 

Usual  Methods— Calculation  of  E.M.F.  Commutation 121 

Calculation  of  Lc— Value  of  "  f  "  by  Hobart's  Method  ...  .  .122 

Interpole  Flux 123 

Interpole  Flux  from  Reactance-voltage — Ampere-turns  for  the  Interpole — 

Interpole  Loss — Resistance  Commutation 124 

Effect  of  Self-induction  .  .  . 125 

Reactance  Voltage  .  .  126 

Example  ....  127 

Output  and  Linear  Reactance  Voltage — Machine  Dimensions  and  Reactance 

Voltage — Machine  Output,  Dimensions,  and  Reactance  Voltage  .  .  128 

Limits  of  Linear  Reactance  Voltage — Properties  of  Brushes  ....  129 
Pressure  Drop  due  to  Contact  Resistance — Machine  Dimensions  limited  by 

Reactance  Voltage 131 

Minimum  Size  for  Large  Generators — Commutation  Losses  .  .  .  132 

Friction  Losses — Commutator  Dimensions 133 

Number  of  Segments  covered  by  the  Brush — Number  of  Brushes  per  Arm — 

Various  Commutation  Limits— Example  of  Commutator  Design        .         .  135 


CHAPTER    X 

INSULATION 

Insulating  Materials — I.  Insulators  with  Good  Mechanical  Qualities  .  .  137 
Varnishes— II.  Insulators  with  Very  High  Dielectric  Strength  .  .  .138 

Insulation  of  Round  Wires 139 

Space-factor  of  Field  Coils — Examples  of  Field-coil  Insulation — Metal  Spool — 

Taped  Coil 141 

Railway-motor  Field-coil.  Fire-proof  Construction.  Strip  Wound — 4,  Traction 

Motor  Field  Coils— Ordinary  Construction 142 

Space-factor  of  Armature  Slots  .........  143 

General  Values  of  Slot  Space-factor 146 

Insulation  between  Armature  Laminae — Insulation  of  Brush-gear  parts, 

Terminal  Blocks,  etc. — Commutator  Insulation 147 


CHAPTER    XI 

GENERAL  MECHANICAL   CONSTRUCTION 

Field-Magnets        .         ..        .     ,  ,         .         .         .    ,     .         .         .         .         .149 

Fixing  of  Field  Coils 150 

Fixing  of  Interpoles — Machining  of  Field-magnets 151 

End-plates  and  Bearings          ..........  152 

Proportions  of  Journals  and  of  Bearings .         . 154 


TABLE   OF   CONTENTS  xiii 


Shafts — Bending  Moment       .         .       .  . 

Combined  Bending  and  Twisting    ...... 

Armature  Construction  ........ 

Radial  Ventilation  through  Armature — Strength  of  Spider  Spokes 
Armature  End  Connections    ....... 

Fixing  of  Armature  Coils 

Commutator  Construction      .         .         .         .         .... 

Brush  Gear  . 


PAGE 

156 
157 
159 
161 
162 
163 
164 
165 


Brush-holders        , .         .         .166 

CHAPTER  XII 
COSTS 

Labour :  1.  Machinemen 170 

2.  Bench-hands  —  Material — Miscellaneous — Calculation  of  Total  Works  cost        171 

Examples  of  Costing      .         .                  .         .         .         .         .  172 

Values  of  Cost-ratios      .         .         .         .         .         .         .         ;  •            173 

Costs  of  Effective  Material .         .  '           174 

Other  Methods  of  Costing — Cost  of  Component  Parts       .         .  175 

Cost  of  Commutators — General  Effects  of  Design  Ratios  upon  Cost  176 

Tendency  of  Modern  Manufacture 180 


EXAMPLES  OF  PROCEDURE  IN  DESIGN 

Constant  Pressure  Machines.    Problem  1 182 

General  Relationships  in  Terms  of  d — Division  of  Voltage  and  Current     .         .  183 

Commutator 185 

Check  against  Brush  Surface — Division  of  Losses — Temperature-rise.    Armature  186 
First  Approximation  to  Field  Ampere-turns  per  pole — Armature  Cross  Ampere- 
turns  per  pole           ...........  187 

Approximate  Weights  and  Costs  of  Effective   Material — Criticisms  of  First 

Design — Alterations  to  reduce  the  Cost     .         .         .         •         .         .         .  188 

Armature  Turns  and  Voltage .         .         .         .         .         .         ...         .         .  189 

Arrangement  of  Slot — Arrangement  of  Conductors  in  Slot         .         .         .         .  190 

General  Conclusion— Final  Calculations — Range  of  Outputs     .         .         .         .  192 

Interpoles 193 

Application  to  13-H.P.  Motor — Armature  Output     ......  194 

Output  of  the  Five-turn  Armature 195 

Interpole  Loss — Losses  and  Efficiency — Possibility  of  enclosing—Effect  on  Costs  196 

Final  Calculations.    Problem  2 — Type  of  Armature  Winding  ....  197 

Deductions  from  Standard  Makers — Assumed  Densities,  etc.    ....  199 
Total  generated  E.M.F. — Relationship  of  D  and  L — Depth  of  Slot — Important 

Ratios— Value  of  X 200 

Losses  .         .      • .         ,         .  .201 

Variable  Losses .  202 

Number  of  Teeth  .         .         .         .         .         .         .         .    .     .         .         .         .204 

Choice  of  Slot  Dimensions — Maximum  Slot-area     .         .                        ,-    .         .  205 

Slot  Insulation— Space  Factor— Losses 206 

Field-dimensions — Gap    Ampere-turns — Teeth     Ampere-turns — Armature-core 

Ampere-turns— Field-coil  Dimensions       .          .         ....         .         .  207 

Yoke  Dimensions — Interpole  Dimensions        .         .          .         .         .          .         .  208 

Interpole  Ampere-turns          .         . 209 


xiv  TABLE   OF   CONTENTS 

PAGE 

Approximate  Cost  of  Net  Effective  Material — Final  Design       .         .         .         .  210 

Principle  on  which  Constant-current  Machines  work 211 

Design  of  Constant-current  Machines — Movement  of  Brushes — Series  Motors    .  212 

Traction  Motors— Limiting  Dimensions          .                            ....  213 

Type  of  Winding — Poles — Temperature-rise — Commutation  Limits           .         .  214 

Division  of  Losses .         .  215 

Binding  Wires — Armature  Core-heads  or  End-plates        .         .         .         .         .  216 

Commutator 217 

Field  Magnet — Yoke  Dimensions — Losses — Field  Ampere-turns       .         .         .  218 

Field  Coil .219 

APPENDIX 

I.  Relationship  between  Depth  of  Slot,  Diameter  of  Armature,  and 

Magnetic  Densities      ........  223 

II.  The  Connection  between  the  Efficiency  of  the  Machine  and  the 

Resistances  of  the  Circuit    .                            .  224 


III.  Calculation  of  Leakage  Flux 

IV.  Relationship  between  Length  and  Depth  of  Field-Coil  (lc  and  de) 

Fig.  14  

V.  Theory  of  Pure  E.M.F.  Commutation 

VI.  Armature-dimensions  and  Reactance-voltage 

VII.  Wire  Tables 

VIII.  Specific  Resistance  of  Copper  at  Various  Temperatures 


226 

230 
231 
232 
234 
235 


INDEX  .       ....  236 


LIST   OF    FIGURES 

FIGUKK  PAGE 

1.  Standard  Multipolar  Field-magnet  with  Armature    .         .         .<        .  .         2 

2.  Arrangement  of  Field-magnet  with  Interpoles  .         .         .         .  facing  p.  2 

3.  Standard  Armature  and  Commutators ,,2 

4.  Standard  Armature  and  Commutators      .         .          .          .         .       -. -.•'  ,,        2 

5.  Curves  of  Permeability .„..•;.        ,,  .         3 

6.  Saturation  Curves  .         .         .         .         .         .         .        '«,...  .         4 

7.  Methods  of  Field  Construction         .         .         .          .         .'       *         *  .         5 

8.  Arrangement  of  Tip  to  avoid  Magnetic  Joints  .         .,.-.,'      ^  ..  .      .   ,      •        6 

9.  Arrangement  of  Hollow  Pole  .         .         ...         .         .         .  .         6 

10.  Lahmeyer  Field  Magnet          .         .         .         .         ,         .         .         .  .         9 

11.  "  Manchester "  Field-magnet           .         .         .         .         .         .         .  .         9 

12.  Overtype  Magnet .        .    '     .       10 

13.  Average  Values  of  Air-gap  Lengths                              ,         .         .          .  .       14 

14.  Permeability  of  Lohys  and  Stalloy           .         .     •    »        »         .         .  .17 

15.  Stalloy  Hysteresis  and  Eddy-current  Losses  for  various  Densities  in  Lines 

per  Square  Inch        .         •    )'    •         •         •         •        -       •"••        *  •       18 

16.  Iron  Losses  at  Various  Densities     .         .....         .         .         .  .19 

K.W. 

17.  Curve  between     /^-^r^  and  Efficiency           .         .                  .         .  .26 

^/±v  .Jr.M. 

18.  Curve  between  KW.  and  Efficiency          .         .         .         .         .         .  .27 

19.  Curve  of  B.H.P.  and  Efficiency       .         .         ...                  .  .28 

20.  Curve  of  Shunt  Field  Loss .     •     .  .31 

21.  Curve  of  C2R  Loss  in  Armature       .         .     '   .         .         .         .         .  .33 

22.  Obsolete  Bipolar  Machine  (Crypto  Electrical  Co.)     .         .         .         facing  p.  34 

23.  Modern  Bipolar  Machine  (Crypto  Electrical  Co.)       ...  ,,34 

24.  Example  of  a  Magnetic  Current       .         .         .         .....  .37 

25.  Magnetic  Circuits  in  a  Multipolar  Machine      .         ,         .         .         .  .38 

26.  Equivalent  Air-gap                   .         .         .         .         .         .         >         ,  .41 

27.  Ampere-turns  for  High  Densities     .         .         .         .         .         .         .  .43 

28.  Ampere-turns  for  High  Densities     .         .         .         .         ..."  .       47 

29.  Slot  Leakage ,         ,         .         i         .  .       47 

30.  Slot  Leakage— Lines  under  Pole-face       .         •         •         ••        .         .  .       48 

31.  Magnetization  Curve       .         .         .         .         .         ...         .  .       49 

32.  Distribution  of  Armature  Field       .         .         ,         .         ...»         .  .       51 

33.  Vector  Diagram  of  Armature  Reaction    .          .         .         *         .         .  .51 

34.  Vector  Diagram  of  Armature  Reaction     .         .....    i      .-•:;      .    .  .       52 

35.  Brushes  in  True  Neutral  Position    .         .         .                   «         .         .  .52 

36.  Cross  and  Back  Ampere-turns          .         .         .      ,  .      .  .-  .    .         .  .       53 

37.  Resolved  Armature  Reaction  .         .         .   '     ..     ;    .         .         .         .  .       53 

38.  Armature  Reaction  in  Multipolar  Machine       .         .         ....  .55 


xvi  LIST   OF   FIGURES 

FIGURE  pAG1, 

39.  Curve  of  compensating  AT .56 

40.  Heating  and  Cooling  Curves  of  a  15  H.P.  D.C.  Motor  for  Different  Loads  .       64 

41.  Field-coil  on  Sheet-metal  Former 72 

42.  Field-coil  on  Cast-iron  Former        ...  .  ,               .73 

43.  Taped-compound  Coil .78 

44.  Field-coil  Diagram .73 

45.  Field-coil  divided  for  Ventilation    .         .         ...         .         .         .       74 

46.  Cooling  Surface  of  Armature.     Method  3 81 

47.  Permissible  Kilowatts  Loss  in  Armature — As  a  Function  of  the  Core  Size 

for  Small  Machines  .  83 

48.  Permissible  Kilowatts  Loss  in  Armature — As  a  Function  of  the  Core  Size 

for  Large  Machines  .         .         .         .  .         .         .         .         .83 

49.  Heating  of  totally  enclosed  Motors  ........       88 

50.  Bi-polar  King  Armature          .         .         .         .         .         .         .         .         .       90 

51.  Diagram  of  King  Armature     .         .         . 91 

52.  Bipolar  Drum  Winding  .         .         .         .  .      «  .         .         .         .       93 

53.  Simple  Multipolar  Drum  Winding  .         .         .... 95 

54.  Developed  Lap-winding 96 

55.  Duplex  King  Winding     .         .         .         .         .   v     .         .         .         .         .97 

56.  Doubly  Ke-entrant  Lap  Winding 98 

57.  Duplex  Singly  re-entrant  Ring  Winding  .         ".''    ' 100 

58.  Duplex  Singly  re-entrant  Drum  Winding 102 

59.  Interpole  Machine  showing  Equalizer  Rings  (Pho3nix  Dynamo  Co.)  facing  p.  104 

60.  Simple  Wave  Winding 105 

61.  Wave  Winding  developed        .         .         . 106 

62.  Wave  Winding  developed         .         .         .         . 106 

63.  Connection  of  Lap-wound  Armature  Coil 110 

64.  Two-circuit  Armature  Coil      .         . 110 

65.  Method  of  Numbering    .         .         .         . Ill 

66.  Lap-wound  Four-pole  Drum  .  112 

67.  Wave- wound  Six-pole  Drum    .         ...         .       '..         .         .         .         .113 

68.  Grouped  Coils 114 

69.  Appearance  of  Lap-winding     .         .  .         .         .         .         .         .     115 

70.  Appearance  of  Wave-winding  ....  ...     115 

71.  Wave-wound  Armature  . facing  p.  104 

72.  Commutation  in  a  Ring  Armature  . 117 

73.  Curves  of  E.M.F.  and  Current  per  Conductor 117 

74.  Fall  of  Current  in  Conductor  undergoing  Commutation    ....     118 

75.  Resistance  Commutation        .         .         .    „    .         .         •         .         .         .     119 

76.  Sayers  Winding .         .         .         .         .120 

77.  78,  and  79.    Aids  to  Commutation     .         .         .         ...         .         .121 

80.  Curve  for  E.M.F.  Commutation  Calculation     .  .         .         .     123 

81.  Process  of  Linear  Commutation .     125 

82.  Morganite  Brushes          .         ...  .         .         .         .         .130 

83.  Battersea  Carbon  Brushes       ......  .     130 

84.  Morganite  Brush  Contact  Losses  in  Watts  per  sq.  inch  with  varying 

Densities  and  Speeds        .         .         .         •         .         .         .         .         .     134 

85.  Taped  Field-coil .       facing  p.  150 

86.  Arrangement  of  Wire  and  Former  Windings  in  Slot          .  .         .143 

87.  Section  through  Slot  of  a  Traction  Motor       -  .         .         .         .         .         .     144 


LIST   OF   FIGURES  xvii 

FIGURE  PAGE 

88.  Space-factors  of  Bound  and  Rectangular  Conductors       ....     145 

89.  Arrangement  of  Bar  Windings  in  Slot    .......     145 

90.  Pole-piece  Lamination ...         .149 

91.  Laminated  Pole-piece  ..........     150 

92.  General  Arrangement  of  Field-magnet  (Cramp)       .         .         .       f&cing  p.  150 

93.  Detailed  Sketch  of  Ventilated  Field-Coil  (Cramp)  .         .         .         .         .150 

94.  Interpole  and  Main- Pole  (Lawrence  Scott)      .         .         .  .         .     151 

95.  Phoenix  Patent  Interpole .         .         .     151 

96.  American  Standard  Bed-plates  for  Direct  Connection      .         .         .  152 

97.  Machine  with   End-plate    and    Yoke    cast    together   (General  Electric 

Company)         ........         .         .         .         .       facing  p.  150 

98.  10-KW.  Motor       .         .         .''.,.         .         ...         .         .154 

99.  Detail  of  Motor-bearing  (Jones)      .         .         .         .         ...,.,:.     155 

100.  Detail  of  Dynamo -bearing  (Jones)  ,   -     .         .         .         ,         ,         .     155 

101.  Section  through  Part  of  Fig.  100   .         .       -.         ..       .         .         ...     156 

102.  Traction  Motor  Armature  Disc       .         ...         .....       .         .     158 

103.  End-plate  or  "  Core-head  "  (Jones) 159 

104.  Armature-core,  End-plates  and  Ventilating  Ducts  (Verity's,  Ltd.)  facing  p.  158 

105.  106.     Details  of  Armature  (British  Thomson-Houston  Co.)         .  .     160 

107.  Armature-core  and  Spider  (British  Westinghouse  Co.)      .         .       facing  p.  158 

108.  Distance-piece  (British  Thomson-Houston  Co.)       .  *  .         .         .     161 

109.  End  Connections        ' ;     .         .         .         .162 

110.  Cylinder-wound  Armature  with  Commutator  (General  Electric  Co.)  facing  p.  164 

111.  Half-section  through  Small  Commutator  (Thomson-Houston  Co.)   .         .     164 

112.  Details  of  a  Commutator  (Cramp)  .         .         ...      •   .  ,  •    .       facing  p.  164 

113.  Commutator  Segment  .         .         .         ....         .....     165 

114.  Commutator  Segment  and  Risers  .         .         .         ....         .     165 

115.  Brush-gear  for  Small  Machine  (General  Electric  Co.)       .         .       facing  p.  166 

116.  Details  of  Small  Brush-rocker 166 

117.  Brush-gear  for  Large  Machine  (General  Electric  Co.)      .         .       facing  p.  166 

118.  150-K.W.  Generator      .         .         .         .       s.;      •         •         •         •         .167 

119.  Detail  of  Brush-rocker  Insulation. 168 

120.  Standard  Brush-holders  (Verity's,  Ltd.)          .         .         .         .       facing  p.  168 

121.  Details  of  Verity  Brush-holders     .         .         . 169 

122.  Method  of  deciding  Best  Yoke-section    .         ...         ....         .  179 

123.  Sketch  of  Interpole  and  Shoe         .  ,      .         .,        .         ...         .         .  195 

124.  Modern  Motor  with  Ball  Bearings  and  Forced  Ventilation      .  .      .         .  198 

125.  Series  Characteristic      .         .         .         .       ,  i       ...         .......       .  211 

126.  Shunt  Characteristic     .         .         .         .,      .  .      .     :    .  ,      ...         .  211 

127.  Series-wound  Generator  with  Arc  Lamps  in  Series          .         .  s      .         .  211 

128.  Constant-current  Characteristic     .      ,..-..».      .         .         .         .         .  211 

129.  Traction  Motor.    Armature  Details        .         .       '..        .         .         .         .  215 

130.  Armature  Slot  Details  .         .         .         .         .         .        -.         .         .  216 

131.  Traction  Motor  Field-coil.  Sketch  of  Details        .  .         .  .      .  .      .  219 

132.  Leakage  Flux.  Case  I -      ..  .         ..:-?-.  226 

133.  Leakage  Flux.  Case  II.  ......         ........  ...      |;       .         .  226 

134.  Leakage  Flux.  Case  III.  .         .         .        ~.         ..•...-.,.  227 

135.  Leakage  Flux.  Case  IV.  .       -.         .       ...  .  ...  -..,..,      .  227 

136.  Leakage  Flux.  Case  V.  .         ...         .         ...  ....         .  228 

137.  Leakage  Flux.  Case  VI.  .         ...  A-    ..;.:..  ...j,      .       ..."      .  229 


LIST    OF    SYMBOLS 

NOTE.— Wherever  the  use  of  symbols  could  be  avoided  without  objectionable 
complication  of  the  printing,  this  course  has  been  followed  ;  and  even  when  symbols 
are  used  in  the  text  their  meaning  is  often  repeated,  so  as  to  reduce  the  necessity  for 
reference  to  the  list  below.  The  symbols  used  in  the  text  are  all  given  here,  but  in 
the  Appendices  it  has  been  necessary  to  make  use  of  a  few  more,  which  are  carefully 
explained  where  they  occur.  All  dimensions  are  in  English  measure. 

A  with  suffix,  as  AOT  (p.  75).    The  area  of  a  particular  part  or  section  in  square  inches.. 

a  A  constant  in  the  temperature  formula  (p.  80)  (except  in  Fig.  26). 

B  Bending  moment  in  inch-lbs.  (p.  157). 

b  A  constant  in  the  temperature  formula  (p.  80)  (except  in  Figs.  26  and  30). 

6t  Width  of  spider  spoke  parallel  to  shaft  (p.  161). 

C  The  total  current  in  amperes  taken  from  or  given  to  a  machine  (p.  128). 

Ch  The  heating  coefficient  of  magnet  coils  (p.  70). 

Cw  The  current  in  any  armature  conductor  in  amperes. 

D  The  outside  diameter  of  the  armature  in  inches. 

d  The  diameter  of  the  pole-core,  or,  in  the  case  of  square  poles,  the  length  of  a  side 

of  the  square,  in  inches. 

dc  The  depth  of  a  coil  in  inches  (p.  73,  Fig.  44). 

E  E.M.F.  in  volts  (p.  128). 

e  The  commutating  E.M.F.  in  volts  (p.  121). 

/  The  flux  set  up  in  one  turn  of  the  coil  by  one  ampere  flowing  therein  (p.  122). 

g  The  number  of  coils  short  circuited  by  a  brush'(p.  122)  (except  Fig.  26). 

K  Used  generally  for  various  constants, 

fej  Thickness  of  spider  spoke  at  its  smallest  section  (p.  161). 

L  The  gross  length  of  an  armature  core  in  inches. 

L,.  The  coefficient  of  self-induction  of  an  armature  coil  under  commutation  (p.  122). 

Le  Length  of  armature  over  end  connections  (p.  162). 

I  The  net  length  in  inches  of  an  armature  core. 

le  Length  of  field  coil  (p.  73,  Fig.  44). 

in  The  number  of  armature  windings  (p.  99). 

m-i  The  ratio  width  of  slot :  width  of  tooth  at  the  armature  periphery  (p.  15). 

w2  The  fringing  factor  (p.  15). 

N*  The  flux  per  pole  in  C.G.S.  lines  (p.  17). 

n  The  revolutions  per  second  of  the  armature. 
P  (with  different  suffixes).    Lost  power  in  watts  (pp.  72  and  80). 

p  The  number  of  poles. 

q  Ampere-conductors  per  inch  of  armature  periphery  (p.  22). 
B,  (with  different  suffixes).    Resistance  in  ohms  (pp.  26  and  27). 

r  Resistance  of  the  circuit  of  a  coil  under  commutation. 


LIST   OF   SYMBOLS  xix 

S        The  number  of  sections  in  a  commutator. 

T°      Temperature  in  degrees  Centigrade. 

T        On  pages  64  and  65  the  time  constant,  and  on  p,  157  twisting  moments. 

t         Instantaneous  values  of  time  (p.  65). 

tc       The  time  of  commutation  in  seconds  (p.  118). 

V       Special  values  of  E.M.F.  (pp.  116  and  125). 

Vfc      Reactance  voltage  according  to  Hobart  (p.  127). 

Vr      Linear  reactance  voltage  (p.  127). 

v        Linear  circumferential  velocity  of  the  armature  in  feet  per  minute  (p.  80). 

w       Total  number  of  armature  conductors. 

X       The  "  electric  loading  "  of  the  armature  (p.  21). 

x        Reactance  in  ohms  of  a  coil  under  commutation  (p.  127). 

Y       Magnetic  loading  of  the  armature  (p.  21). 

y        The  number  pitch  of  an  armature  winding  (p.  94). 

2//       Forward  number  pitch  (p.  94). 

7/7,      Backward  number  pitch  (p.  94). 

GREEK  LETTERS. 
a        Modulus  of  elasticity  (p.  157) ;   also  as  an  angle  (p.  162),  as  a  temperature 

coefficient  of  copper  (p.  67),  and  as  cross-section  of  a  conductor  (p.  96). 
,8  (with  various  suffixes).    Density  in  lines  per  square  inch  (p.  38). 
e         Base  of  the  natural  logarithms  (p.  121). 
7;  (with  various  suffixes).    Efficiency  (pp.  26  and  27). 
0        Temperature  in  degrees  Centigrade  (p.  65)  in  particular  cases. 
A        Leakage  factor  (p.  44). 
p        Specific  resistance  of  copper. 

ABBREVIATIONS. 

L.M.T  (with  various  suffixes).    Length  of  mean  turn. 

t.p.s.         Armature  turns  per  commutator  section. 

K.W.     Kilowatts. 

H.P.      Horsepower. 

~  Frequency  in  cycles  per  second. 

S.W.G.  Standard  wire  gauge. 

A.T.       Ampere-turns. 

D.C.C.  Double  cotton  covered. 

S.C.C.    Single  cotton  covered. 

P.p.         Pole-pitch. 


ERRATA 


Page  13,  line  28,  for  3000  read  30,000. 

r*  (* 

,    21,  Table  I.,  for  •=  read  s. 
D  b 

„     22,  for  DpA  read  5!. 

,,     26,  line  2,  for  "  shunt  "  read  "  shunt  or  compound." 

„    43,  Formula  (6),  for  7D  read  0«7D. 

,,43,        „        (c),  for  5-3D  read  0-53D. 
Pages  47  and  48,  for  6986  read  6786. 
Page  60,  line  26,  "  the  armature  of  a  dynamo." 

„     61,  line  25,  for  "  15  "  read  "  13." 

„    76,  equation  (2),  for  285  read  275,  and  multiply  the   expression  by 

|  (of.  p.  230). 

„     77,  line  9  and  equation  (2),  for  142-5  read  137'5. 

4. 
,,    77,  equation  (2),  multiply  by  -  (cf.  p.  230). 

„    82,  line  33,  for  42  read  47. 

„  112,  line  1,  for  "  it  is  5  "  read  "  it  is  6." 

„  112,  line  2,  for  (yf  -  1)  read  (yf  ±  1). 

„  127,  line  32,  for  (t.p.s.)  read  (t.p.s.)-. 

„  |£,1   fig.  118,  "scale  1"  =  1'"  delete. 

„  176,  line  38,  for  "ampere-turns  per  pole  "  read  "  flux  per  pole." 

„  208,  Equation  (1),  read  450  =  4'7dc2  +  47(k  +  dc)  +  Q-28L.dc. 

„  223,  read  wt  +  wt  =  irD/t. 

,,  233,  line  16,  for  "  turns  "  read  "  lines." 


CONTINUOUS    CURRENT    MACHINE 

DESIGN 

CHAPTER   I 
THE  FORM  OF  MODERN  MACHINES 

Introduction. — All  continuous-current  machines,  whether  motors  or 
dynamos,  consist  of  three  main  parts,  namely — 

(1)  The  field-magnet. 

(2)  The  armature. 

(3)  The  collecting  gear. 

It  is  the  business  of  the  designer  so  to  construct  and  proportion 
these  parts  as  to  obtain  the  best  results  for  a  given  expenditure  of 
capital  outlay  as  well  as  of  energy ;  further,  it  is  his  work  to  fit  them 
together  and  to  arrange  them  in  their  proper  relative  position  by 
means  of  suitable  mechanical  devices. 

In  considering,  therefore,  the  design  of  continuous-current  machines, 
we  shall,  first  of  all,  set  forth  the  laws  governing  the  proportions  of 
the  main  parts,  and  later  give  some  examples  of  the  design  of  the 
main  mechanical  supports  and  attachments.  It  is  impossible  to 
separate  entirely  the  electrical  and  magnetic  design  from  that  which 
is  purely  mechanical ;  for  very  often  it  happens  that  the  one  partly 
determines  or  limits  the  other,  and  such  instances  will  be  brought 
out  as  the  work  proceeds. 

General  Forms. — Now,  because  the  function  of  a  well-designed 
magnetic  circuit  is  to  allow  of  the  existence  of  a  magnetic  flux  with 
as  little  reluctance  as  possible,  the  modern  machine  is  arranged  in 
one  of  the  various  forms  depicted  in  Figs.  1  to  4.  The  most  important 
of  these  is  the  shape  shown  in  Figs.  1  and  2,  and  the  remarks  which 
follow  will  always  be  made  with  reference  to  such  a  machine  unless  the 
contrary  is  definitely  stated. 

In  the  case  of  small  machines,  the  over-all  dimensions  and  the 
proportions  for  a  given  output  are  dictated  by  questions  both  of 
economy  and  appearance,  while  in  the  larger  sizes  economy  is  usually 
the  ruling  factor. 

B 


2        CONTINtJOUS^CtrR^ENT   MACHINE   DESIGN 

Present  Practice. — Whatever  machine  we  examine  we  find  that, 
as  the  field-magnet  shajie  has  become  practically  standardized  to  the 
form  shown  in  Figs.  1  or  2,  so  the  armature  is  practically  standardized 


FIG.  1. — STANDARD  MULTIPOLAR  FIELD-MAGNET  WITH  ARMATURE. 

to  the  general  shape  of  Fig.  3,  while  the  commutator  is  as  shown  in 
Figs.  3  and  4. 

Form  of  Field-magnets. — The  form,  however,  of  all  these 
parts  is  affected  by  the  material  to  be  used  for  their  manufacture. 
In  the  case  of  field-magnets  the  materials  adopted  are  cast  iron, 
wrought  iron,  mild  cast  steel,  and  malleable  iron. 

Cast  Iron  is  a  material  of  low  magnetic  permeability,  but  also 
of  low  cost. 

Cast  Steel  and  Wrought  Iron  are  comparable  in  respect  both 
of  cost  and  of  permeability. 

Some  relative  values  of  permeability  in  the  respective  cases  are 
shown  by  the  curves  given  in  Figs.  5  and  6,  which  are  obtained  from 
average  samples  of  the  different  materials ;  from  these  it  will  be  seen 
(since  the  cost  of  cast  iron  is  about  f  that  of  cast  steel,  while  the 
relative  induction  of  the  former  to  the  latter  for  a  given  number  of 
ampere-turns  is  about  as  5  is  to  3)  that  for  cases  like  the  yokes 
of  field-magnets,  where  no  copper  surrounds  the  iron,  the  question  of 
material  resolves  itself  into  one  of  weight  and  mechanical  strength, 
and  not  of  cost. 

Those  parts  of  the  magnet-frame  which  are  surrounded  by 
copper  must  be  so  designed  as  to  carry  the  maximum  flux  while 
having  the  minimum  perimeter,  i.e.  they  must  be  made  of  material 
of  the  highest  permeability ;  and  also  they  must  be  of  such  a  shape 


G.  2.— ARRANGEMENT  OP  FIELD- MAGNET  WITH  INTERPOLES. 


FIGS.  3,  4.— STANDARD  ARMATURE  AND  COMMUTATORS. 


[To  face  p.  2. 


THE   FORM   OF   MODERN   MACHINES  3 

as  to  give  maximum  sectional  area  with  minimum  perimeter, 
i.e.  their  section  should  be  nearly  circular.  Thus,  except  in  special 
instances,  cast  iron  is  inadmissible  for  field-poles. 

Wrought  Iron  is  a  material  of  high  permeability,  but  it  does 
not  lend  itself  to  special  shapes.  Circular  poles  are  rarely  made  of 
wrought  iron  ;  but  this  material  has  the  great  advantage  that  it  can 


Cast  Steel 


Wrought 

Iron 

(Hopkinson) 


Grey 
Cast  Iron 
(Hopkinson) 


20 


40          60  80         100        120        140 

AMPERE  TURNS  PER  INCH  LENGTH. 

FIG.  5. — CURVES  OF  PERMEABILITY. 


160 


easily  be  obtained  in  thin  sheets,  or  laminae,  and  in  this  form  it  is 
usually  used  to  build  up  rectangular  or  square  poles. 

Where  it  is  desired  to  cut  down  to  a  minimum  the  eddy-currents 
in  poles  and  pole-shoes,  these  laminae  are  adopted  either  for  the 
complete  pole  and  shoe  or  for  the  shoe  alone.  Examples  of  these 
constructions  will  be  given  later. 


4        CONTINUOUS   CURRENT   MACHINE   DESIGN 


THE  FORM   OF  MODERN   MACHINES  5 

Cast  Steel  has  the  two  advantages  of  possessing  high  permea- 
bility and  of  being  easily  cast ;  it  is  therefore  very  suitable  for  magnet 
frames  made  complete  with  their  poles,  the  latter  being  then  generally 
circular  or  oval  in  section. 

Malleable  Iron  has  a  permeability  midway  between  cast  iron 
and  cast  steel ;  but  its  cost  is  practically  equal  to  that  of  the  latter, 
and  its  only  compensating  advantage  is  that  often  readier  delivery 
can  be  obtained,  especially  for  small  or  complicated  shapes.  It  is 
therefore  only  used  where  urgency  dictates. 

Field-poles. — In  the  construction  and  fixing  of  field-poles,  there 
is  a  choice  of  several  methods.  The  pole  may  be  cast  with  the  yoke, 


I.  Mild  Steel  Pole  cast  into  Cast-Iron  Yoke  and  fitted  with  Shoe. 
II.  Mild  Steel  Pole  cast  into  Cast-Iron  Yoke  and  fitted  with  Laminated  Shoe 

III.  Laminated  Pole  and  Shoe  fitted  to  Cast-Steel  Yoke. 

IV.  Pole  and  Yoke  made  in  Cast  Steel  and  Shoe  fitted  as  in  I. 

FIG.  7. — METHODS  OP  FIELD  CONSTRUCTION. 

in  which  case  the  poles  must  be  made  either  of  cast  steel  or  of 
malleable  iron  if  the  field  copper  is  to  be  reduced  to  a  minimum ;  or 
the  steel  pole  may  be  fixed  separately,  in  which  case  there  is  an  extra 
surface  to  machine ;  or  stampings  may  be  riveted  together  and  fixed 
into  the  yoke  when  the  section  or  shape  of  the  pole  is  limited,  as 
mentioned  above. 

Examples  of  various  constructions  are  seen  at  I,  II,  III,  IV,  Fig.  7. 

In  all  cases,  because  the  pole  must  be  small  (to  keep  down  the 
amount  of  copper),  a  shoe  must  be  used  to  reduce  the  air-gap  density ; 


CONTINUOUS   CURRENT  MACHINE   DESIGN 


FIG.  8. — ARRANGEMENT  OF  TIP  TO  AVOID 
MAGNETIC  JOINTS. 


and  it  is  in  satisfying  these  two  conditions  that  the  high-permeability 
pole  is  of  such  use  and  importance. 

Machines  without  Pole-tips. — All  sorts  of  constructions  have 
been  used  to  obviate  the  necessity  for  the  pole-tip;  thus,  for  instance, 
one  maker  casts  pole,  shoe,  and  yoke  all  in  one.  He  then  gets  his 
field-coil  on  by  having  the  tip  all  on  one  side  of  the  pole  (Fig.  8). 

Similarly,  some  makers  cast  the 
pole  hollow,  and  put  the  large 
field-coil  on  as  shown  in  Fig.  9.* 
In  each  case  the  object  is  to  get 
rid  of  the  joints  in  the  frame, 
and  at  the  same  time  to  keep 
down  the  weight  of  field-copper. 
As  regards  ordinary  methods,  the 
four  illustrated  in  Fig.  10  are 
typical ;  and  from  these  it  is  seen 
that  a  butt  joint  may  be  arranged 
either  between  pole  and  shoe,  or 
pole  and  yoke,  but  it  is  advisable 
not  to  have  butt  joints  at  both 
these  places ;  for  the  effect  of  joints  in  the  magnetic  circuit  is  always 
to  increase  the  reluctance  of  the  path,  this  increase  depending  upon 
the  badness  of  the  fit.  Even  with  an  apparently  perfectly  fitted 

joint,  an   additional  reluct- 
ance   is   introduced,   which 
has  been  estimated  as  corre- 
sponding  to   an   air-gap   of 
about  O'OOOo  inch ;   and  in 
addition  to  this,  the  leakage 
factor  is  somewhat  increased. 
Ordinary     Forms     of 
Field  -  construction.  - 
Usually  the  form  that  pays 
best  is  that  with  round  pole 
cast   into   a   C.I.    yoke,    as 
shown    at    I,    Fig.    7,    but 
naturally   this    depends    to 
some   extent  on  the  works 
and  on  the  tools  available. 
The  writer  prefers  to  use  a  cast  steel  or  mild  steel  pole  as  often 
as  possible,  believing  that  to  be  the  most  economical  arrangement, 
especially  in  small  machines.  The  length  of  the  armature-stampings  is 
therefore  limited,  where  possible,  to  allow  the  use  of  a  round  steel  pole. 

*  See  "  Magnetic  Leakage  and  its  Efiect  in  Electrical  Design,"  Proc.  Inst.  Elec. 
Eng.,  vol.  38,  No.  183. 


FIG.  9. — ARRANGEMENT  OF  HOLLOW  POLE. 


THE   FORM   OF  MODERN   MACHINES  7 

Laminated  Poles.  —  We  have  previously  seen  that  laminated 
poles  must  be  rectangular  in  section,  and  that  the  coil  around  that 
rectangular  section  needs  a  greater  amount  of  copper  than  would  with 
circular  poles  be  necessary.  But  there  is  a  corresponding  advantage 
in  the  reduction  of  eddy-currents  in  the  poles  themselves.  The  effect 
of  the  iron-losses  (from  eddy-currents  and  hysteresis)  in  continuous- 
current  machines  becomes  more  and  more  obvious  every  day  ;  and  the 
reason  for  this  is  that  makers  attempt  to  use  armature  discs  with 
fewer  and  fewer  slots  in  them.  The  fewer  the  slots  the  less  is  the 
number  of  insulating  tubes,  and  therefore  the  higher  is  the  space- 
factor  for  a  given  winding.  The  fewer  the  slots,  the  greater  the 
difference  produced  in  the  change  of  flux  between  the  teeth  and  the 
slots  ;  so  that,  whereas  with  a  large  number  of  slots  we  have  almost 
a  uniformly  distributed  flux,  in  the  case  of  few  slots  we  have  the 
flux  lines  in  large  bunches,  alternating  with  little  spaces  almost  free 
from  flux.  It  is  this  unequal  distribution  of  flux  which  tends  to  set 
up  eddy-currents  in  the  pole,  and  which  may  be  reduced  by  means 
of  a  properly  laminated  pole.  For  most  cases  the  laminated  shoe 
practically  does  away  with  all  the  eddy-  currents,  and  there  is  no 
sensible  heating  in  the  poles  except  in  the  case  of  traction-motors, 
where  laminated  poles  are  almost  a  necessity. 

Comparison  of  Circular  and  Rectangular  Pole.  —  In  order 
to  bring  out  the  advantage  of  a  circular  pole,  let  us  compare  the  costs 
of  copper  for  a  circular  pole  and  for  a  square  pole  of  the  same  sectional 
area,  say  for  the  following  conditions  :  — 

The  resistance  per  coil  in  each  case  is  to  be  about  180  ohms, 
while  the  voltage  per  coil  is  100,  and  the  ampere  turns  4000.  We 
will  adopt  a  pole  of  50  square  inches  cross-section  ;  then  in  the  case 
of  the  circular  pole  the  diameter  will  be  8  inches. 

Circular  Pole.  —  Now,  for  a  coil  of  this  resistance  a  winding 
depth  of  about  1  J"  is  required  (Chap.  VI.). 

Length  of  mean  turn  then  =  29'85" 

resistance  of  mean  turn  =  J$Q$  =  0*025  ohm 

1Ann  36  x  1000  x  0-025      _1K    , 

and  resistance  per  1000  yards  =  -       —  9Q*ft5  "  =  *0'15  ohms 

From  the  wire  tables  we  find  that  the  resistance  per  1000  yards 
of  No.  21  S.W.G.  is  29  '9  ohms  cold,  or  about  33  ohms  when  warm, 
this  being  the  nearest  size  to  the  above  requirement. 

Hence,  with  this  wire,  which  has  a  diameter  covered  of  0*042"  — 

o 

Turns  per  layer  =  =  190 


Layers  per  coil  =  =  35 


8         CONTINUOUS   CURRENT   MACHINE   DESIGN 

Turns  per  coil  =  190  x  35  =  6650 

-P    .  ,  .,       6650x29-85  x  33      100    , 

Resistance  per  coil  =  --  ^  -  -^r  ---  =182  ohms 

ob  X 


From  the  table  we  find  that  No.  21  S.W.G.  weighs  9-301  Ibs.  per 
1000  yards,  so  that— 

w  .  ,  ,    f  .,       6650x29-85x9-301       ri  Q  ,, 

Weight  of  copper  per  coil  =  -     —  ^  -  Tnru\~     -  =  51'3  Ibs. 

ob  X  luUU 

Square  Pole.  —  If  we  adopt  the  square  pole,  the  winding  depth 
to  fulfil  the  same  requirements  will  be  greater  —  say  2". 

Length  of  mean  turn  =  3  6  -28"  (the  dimensions  of  the  pole  being 
7-07"  x  7-07"). 


Eesistance  per  1000  yards  =  36  X  ^  *  °'025  =  24'8  ohms 

ob'Zo 

The  nearest  wire  is  No.  20  S.W.G.,  which  has  a  resistance  of 
23'6  ohms  per  1000  yards  cold,  i.e.  26  ohms  warm. 

Hence,  with  this  wire,  which  has  a  covered  diameter  of  0*046"  — 

8" 
Turns  per  layer  =  ^^,  =  174 

2" 
Layers  per  coil  =  ,  =  45 


Turns  per  coil  =  174  x  45  =  7830 

T>    .  ,  .-,      7830  x  26  X  36-28      OAC    , 

Kesistance  per  coil  =  --  ^  -   r    --  =205  ohms 


From  the  tables,  No.  20  weighs  11'77  Ibs.  per  1000  yards. 


™-  •  1,4.    f  -i  X  11*77  x  36-28      01  Q  ., 

Weight  of  copper  per  coil  =  -     —  ^-  —  in  -  =  91  '3  Ibs. 

ob  X  1UUU 

So  that,  although  the  resistances  of  these  coils  only  differ  by 
about  12  per  cent.,  the  weight  of  copper  for  the  square  pole  is 
78  per  cent,  greater  than  that  for  the  circular  pole,  and  putting  the 
value  of  copper  and  labour  at  Is.  6d.  per  pound  of  material,  we  effect 
a  saving  of  £3  per  coil  by  adopting  the  circular  section  rather  than 
the  square.  Comparisons  between  circular  and  rectangular  sections 
show  more  and  more  to  the  advantage  of  the  former  as  the  rectangle 
departs  further  and  further  from  the  square.  Thus  a  circular  section 
is  most  economical  ;  and  of  rectangles  the  square  is  best. 

It  would  seem  that  many  designers  hardly  realize  the  bearing  of 
this  calculation,  which  is  of  special  importance  in  the  case  of  small 
machines,  where  the  weight  of  field  copper  is  to  armature  copper  in 
the  proportion  of  about  4  to  1.  This  ratio  decreases  very  consider- 
ably in  large  machines,  so  that  the  question  of  circular  as  against 
rectangular  field-poles,  requires  more  careful  consideration,  especially 
as  the  round  pole  will  often  give  insufficient  cooling  surface.  These 
calculations  are  affected  also  to  a  certain  extent  by  the  question  of 


THE   FORM   OF   MODERN    MACHINES 


leakage  factor ;  where  the  latter  amounts  to  1*4,  it  may  in  certain 
instances  pay  to  design 
a  field  quite  differently.* 
Other  Types  of 
Field  -  magnet.  —  The 
question  of  the  shape  of 
field-magnets  cannot  be 
dismissed  without  a  refer- 
ence to  three  other  types. 
The  first  is  that  known 
as  the  "  Lahmeyer "  ;  it 
is  depicted  in  Fig.  10,  and 
is  the  most  economical 
form  of  bipolar  machine 
yet  designed.  Fashion, 
however,  is  against  it, 
for  it  is  practically  im- 
possible now  to  sell  a 
machine  which  has  other 
than  a  circular  yoke. 

The  second  type  which 
deserves  consideration  is 
known  as  the  "  Man- 
chester" (Fig.  11),  and 

it  has  been  able  to  hold  FIG.  10.— LAHMEYER  FIELD  MAGNET. 

its  own  on  account  of  its 
extreme  steadiness,  due  to  the  low  position  of   the  armature.     It 


FIG.  11. — "MANCHESTER"  FIELD  MAGNET. 

*  See  the  author's  paper  on  "  Magnetic  Leakage  and  its  Effect  on  Electrical 
Design,"  Jour.  I.E.E.,  vol.  38,  pp.  548  et  seq. 


io       CONTINUOUS   CURRENT   MACHINE   DESIGN 

possesses,  however,  the  two  disadvantages  of  large  magnetic  leakage 
and  many  joints  in  the  frame. 

The  third  type  is  the  old  bipolar  machine  (Fig.  12),  which  has 
some  curious  advantages.  In  the  modern  machine,  with  the  poles 
fixed  radially,  the  area  of  the  gap  cannot  be  increased  beyond  the 
dimensions  of  the  pole  unless  a  pole-shoe  be  put  on.  In  this  bipolar 
case,  however,  the  pole-arc  is  largely  independent  of  the  section  of 
the  pole,  so  that  almost  any  area  of  air-gap  may  be  obtained  without 
the  use  of  a  shoe  and  without  increasing  the  pole  sectional  area; 
that  is  to  say,  with  reasonable  air-gap  or  pole  densities  we  may  still 
slip  the  finished  field-coils  over  the  ends  of  the  magnet. 

Multipolar  and  Bipolar  Machines. — The  foregoing  machines 


FIG.  12. — OVERTYPE  MAGNET. 

may  be  summarized  as  follows :  Were  it  possible  always  to  construct 
bipolar  machines,  the  most  economical  dynamo  would  usually  be  found 
to  be  one  having  circular  poles  and  an  armature  whose  length  was  as 
great  compared  to  its  diameter  as  that  field  shape  would  allow. 

In  support  of  this  statement,  we  have  to  consider  the  following 
factors  as  affecting  the  economy  of  field-magnets  : — 

(1)  The  weight  of  copper  on  the  field-magnet,  which  is  determined 
by— 

(a)  the  ampere-turns  per  pole ; 

(b)  the  number  of  poles ; 


THE   FORM   OF   MODERN   MACHINES  n 

(c)  the  length  of  mean  turn  per  coil ;  and 

(d)  the  watts  lost. 

Of  these— 

(a)  The  ampere-turns  per  coil  are  dependent  chiefly  upon 
the  air-gap  length  and  the  tooth  saturation. 

(c)  The  length  of  mean  turn  per  coil  depends  largely  upon 
the  pole  perimeter. 

(2)  The  weight  of  steel  for  the  poles  depends  for  a  given  material 
upon  the  flux-density  in  the  pole,  the  number  of  poles,  and  the 
sectional  area  per  pole,  i.e.  upon  the  total  sectional  area  of  all  the 
poles,  if  the  total  flux  and  the  material  be  known. 

Now,  the  air-gap  length  is  decided  largely  by  mechanical  clearance, 
and  other  considerations  which  are  practically  independent  of  the 
number  of  poles.  Whence,  the  number  of  ampere-turns  per  pole  is 
practically  independent  of  the  number  of  poles. 

It  is  easy  to  see  that  the  geometrical  figure  which  has  the  greatest 
sectional  area  for  least  perimeter  is  the  circle ;  so  that  a  comparison 
of  the  economy  of  bipolar  and  multipolar  fields  may  be  made  on  the 
assumption  of  constant  total  flux ;  watts  lost  and  material  being  the 
same  in  both  cases.  Therefore  the  comparison  is  really  between  an 
area  made  up  of  a  number  of  small  circles  (multipolar)  as  against  one 
large  circle,  i.e.  between  the  perimeter  of  a  circle  of  a  sectional  area 

S,  and  the  sum  of  the  perimeters  of  n  small  circles  each  of  area  =  -, 

n 

which  are  in  the  ratio  of  1  :  ^/n.  Obviously  the  comparison  is 
immensely  in  favour  of  the  bipolar  case. 

It  is  not,  however,  possible  to  construct  large  machines  of  bipolar 
form,  because  of  the  difficulties  of  commutation  and  the  large 
magnetic  leakage.  On  the  other  hand,  small  machines  which  are 
bipolar  are  not  as  economical  as  they  might  be,  on  account  of  the 
necessity  for  the  circular  yoke  imposed  by  public  taste. 

What  has  been  said  above  applies  equally  to  machines  with  one 
field  coil,  like  the  Lundell  motor,  for  a  full  discussion  of  which  the 
reader  is  referred  again  to  the  Proc.  I.E.E.,  yol.  38,  p.  558. 

General  Form  of  Armatures. — Practically  only  one  material, 
viz.  soft  iron  or  very  mild  steel,  is  available  for  armature  cores ;  and 
nowadays  there  is  but  one  shape  of  core  in  use,  viz.  the  slotted  drum. 
Further,  for  both  small  and  large  machines  the  "barrel"  type  of 
winding  is  now  adopted  (Fig.  3),  so  that  unless  some  other  form  is 
specially  mentioned,  the  constants,  etc.,  given  in  this  book  will  refer 
to  machines  having  armatures  exactly  in  accordance  with  this 
description. 

General  Form  of  Commutators. — Nearly  always  the  commutator 


12      CONTINUOUS   CURRENT   MACHINE   DESIGN 

is  of  the  same  general  type  (Figs.  3,  4,  and  111),  and  this  is  charac- 
terized by  the  end-ring,  having  a  small  angle  (of  about  5C)  on 
the  upper  surface  compared  with  the  angle  on  the  lower  side  of 
between  30°  to  40°  (see  p.  165).  Some  designers  prefer  to  keep  the 
upper  side  horizontal.  The  dimensions  are  almost  standardized  now, 
so  that  for  a  given  current  density  at  the  brush  and  a  given  speed, 
there  is  a  constant  temperature  rise;  and  two  machines  of  similar 
output,  although  of  different  manufacture,  will  almost  always  have 
commutators  of  the  same  cylindrical  surface. 

If  it  could  be  proved  to-morrow  that  copper  was  not  the  best 
material  for  commutator  segments  (and  it  is  very  doubtful  whether 
it  is),  then  the  form  and  dimensions  of  commutators  would  change 
immediately. 


CHAPTER  II 

GENERAL  PROPORTIONS  OF  MODERN 
MACHINES 

As  has  been  shown,  choice  of  material  affects  the  question  of  general 
form ;  it  also  dictates  the  general  proportions. 

Having  already  practically  decided  on  the  material  for  the  poles, 
the  armature,  and  in  some  cases  the  yoke,  we  find  that  the  general 
proportions  are  ruled  by  a  number  of  factors.  In  the  case  of  the 
field-magnet,  the  general  determining  factors  are — 

(1)  The  maximum  densities  permissible,  and  the  ratio  of  pole-arc 
to  pole-pitch. 

(2)  The  watts  to  be  dissipated  in  the  field-coils,  and  the  tempera- 
ture-rise of  the  latter. 

(2)  will  be  dealt  with  under  the  heading  of  "  Temperature-Kise." 
From  very  careful  comparison  of  a  number  of  designs,  certain 
densities  have  now  been  adopted  for  continuous-current  machines 
which  are  employed  by  nearly  all  modern  designers. 

Limiting  Densities  :  (i)  Yoke. — If  cast  iron  be  used,  the  density 
varies  from  26,000  to  45,000  lines  per  square  inch.  (It  must  be 
very  soft  cast  iron  for  the  number  of  lines  to  exceed  45,000.)  A 
density  of  from  45,000  to  90,000  lines  per  square  inch  may  be  used 
if  the  yoke  be  of  cast  steel. 

(2)  Pole. — Passing  on  to  the  pole  (which  will  be  of  wrought  iron 
or  mild  steel),  the  density  at  full  load  should  not  exceed  120,000  lines 
per  square  inch,  and  should  for  safety  be  less ;  a  very  fair  value  being 
100,000. 

(3)  Air-gap. — Here  the  densities  used  are  somewhat  more  vague, 
and  depend  very  largely  upon  the  size  of  the  machine.     In  a  small 
motor,  say  5  H.P.,  the  density  in  the  air-gap  is  about  45,000  lines 
per  square  inch,  and  even  less.     In  still  smaller  motors  of  1  H.P.-  or 
less,  300001ines  per  square  inch  is  the  maximum  density  admissible. 
In  large  generators  (500  K.W.)  60,000  is  a  common  figure. 

Air-gap  Length. — The  air-gap  length  cannot  be  reduced  in  pro- 
portion to  the  armature  diameter ;  it  must  not  be  less  than  fs",  nor 
need  it  be  more  than  |"  from  the  point  of  view  of  mechanical  clearance. 


14       CONTINUOUS   CURRENT   MACHINE   DESIGN 


0-25 


0-20 


•-1  0-15 


0-10 


0-05 


The  modern  tendency  is  to  keep  down  the  air-gap  in  larger  machines, 
and  to  this  end  interpoles  contribute,  as  is  evidenced  by  Fig.  13, 
which  gives  average  values  of  the  air-gap  in  modern  practice. 

Relative  Constancy  of  the  Field  Ampere-turns. — In  Fig. 
13  have  been  given  the  usual  modern  air-gap  lengths  for  various 
sizes  of  machine.  If  these  be  multiplied  by  0'313  and  by  the  air-gap 
densities  given  above,  we  have  the  gap  ampere-turns  per  pole  for  each 
size  of  machine.  Similarly,  the  ampere-turns  for  the  armature  teeth 
may  be  approximately  predetermined,  and  the  sum  of  these  two  is 

usually  80-85  per  cent,  of 
the  field  ampere-turns  per 
pole.  It  is  clear  from  the 
air-gap  curves  that  the 
length  of  gap  increases 
very  slowly  with  increase 
of  output,  and  in  conse- 
quence the  ampere-turns 
per  pole  are  relatively 
constant. 

The  Ratio  Pole-arc : 
Pole  -  pitch. — The  next 
factor  that  affects  the  pro- 
portions is  the  ratio  of  pole- 
arc  to  pole-pitch,  which 
is  determined  by  two  con- 
siderations, namely— 

(a)  Relationship  be- 
tween ampere-turns  of 
the  armature  and  ampere - 
turns  of  the  field ;  and 

(6)  Neutral  zone  re- 
quired to  give  good  com- 
mutation. 

Modern  designers  vary 
considerably  in  their  choice 


0          5        10        15        20        25        3' 
ARMATURE  DIAMETER  IN  INCHES. 


35        40 


A  without  interpoles  ;  equation  y=  -06+  -00487  x  nearly. 
B  with  interpoles  ;  equation  y=-036+  -00316  x  nearly. 

FIG.  13. — AVEEAGE  VALUES  OP  AIR-GAP  LENGTHS. 


A  good  average  value  frequently 
considerations   will   influence   the 


of  this  ratio,  as  from  Of6  to  0*85. 
adopted  is  0'7.  The  following 
choice  of  the  ratio : — 

In  small  machines  a  large  ratio  means  a  large  leakage-factor,  which 
is  undesirable ;  further,  the  weight  of  copper  on  the  field  being  so  much 
in  excess  of  that  on  the  armature,  it  is  not  infrequently  possible  to 
cheapen  a  machine  by  increasing  the  diameter  of  the  armature  with- 
out any  alteration  to  the  poles,  i.e.  by  simply  altering  the  ratio  pole-arc 
to  pole-pitch.  To  decide  this  point  it  is  absolutely  necessary  to  taks 
a  mean  ratio,  such  as  07,  and  from  a  trial  design  to  estimate  roughly 


GENERAL  PROPORTIONS  OF  MODERN  MACHINES    15 

the  cost  (see  Chap.  XII.)  ;  then  by  changing  the  ratio  the  cost  may 
be  estimated  anew. 

Armature-teeth.  —  Passing  now  to  the  question  of  armature- 
teeth.  For  a  given  armature-diameter,  the  greater  the  density  in  the 
armature-teeth  the  more  room  is  occupied  by  copper  ;  therefore,  the 
greater  the  density  in  the  teeth  the  higher  is  the  output  of  a  machine 
for  a  given  diameter  of  armature.  Seven  or  eight  years  ago  designers 
advised  a  maximum  density  at  the  roots  of  the  teeth  (on  the  assump- 
tion that  all  the  flux  passed  through  the  teeth)  of  118,000  lines  per 
square  inch,  while  to-day  this  is  sometimes  as  high  as  195,000.  It  is 
advisable  to  keep  the  apparent  maximum  density  in  the  teeth  between 
120,000  and  160,000  lines  per  square  inch,  because  there  is  little 
advantage  in  forcing  up  this  density  beyond  the  point  where  the  curve 
for  the  iron  is  parallel  to  that  for  an  air-gap. 

Now,  if  we  know  the  ratio  of  the  density  at  the  pole-face  to  that 
at  the  roots  of  the  teeth,  also  the  ratio  gross  to  nett  length  of  arma- 
ture-core, then  for  given  ratio  width-of-slot  to  width-  of-  tooth  the  depth 
of  the  tooth  is  determined  in  terms  of  the  armature-  diameter,  thus  :  * 


Depth  of  tooth  =  l  ~  ;f  (*  +       D,  where 
2(1  +  mi) 

„  __  _  density  at  pole-face  _      gross  length  of  armature      1 
~  apparent  density  at  root  of  teeth    k    net  length  of  armature      m2 
m2  being  a  factor  which  allows  for  fringing  at  the  pole-tips,  and 
_  width  of  slot 

~  width  of  tooth  at  armature-face 

The  following  are  some  very  general  values  for  the  different  terms 
in  the  above  equations  :  — 

Density  of  pole-face  =    54,000  lines  per  sq.  in.  )  .  _  1     9  7 

Density  of  root  of  teeth  =  146,000      „        „       „    /*'*  ri 
Eatio  of  net  length  to  gross  length  of  armature  =  0*8 

m/a  =  1*1  mi  =  1 

and  width  of  slot  =  width  of  tooth  at  face 
With  these  values  depth  of  tooth  =  0'04D  * 

Of  these  values,  those  given  for  the  pole-face  and  teeth  cannot 

change  much.     The  ratio  -  length  is  almost  fixed,  as  also  is  m2  : 

gross 

mi  f  has  been  shown  by  Professor  S.  P.  Thompson  to  be  practically  best 
as  unity  or  thereabouts  ;  the  absolute  best  ratio  seems  to  be  such 
that  the  width  of  copper  in  the  slot  is  equal  to  the  width  of  tooth- 
root,  which  however  is  also  in  practical  agreement  with  mi  =  1. 

Number   of  Teeth.  —  The  number  of  teeth  to  be  adopted  is 

*  See  Appendix  I.  t  See  Journal  Soc.  Arts,  vol.  54,  p.  997. 


16       CONTINUOUS   CURRENT   MACHINE   DESIGN 

affected  chiefly  by  two  considerations,  viz.  that  economy  dictates  as 
few  teeth  as  possible,  while  perfect  flux-distribution  and  commutation 
demand  a  large  number  of  teeth. 

It  has  been  shown  that  the  depth  of  the  slots  depends  chiefly 
upon  the  armature  diameter  when  the  ratio  width  of  tooth  to  width 
of  slot  is  fixed.*  From  these  two  factors  the  total  aggregate  slot 
area  is  settled,  and  the  smaller  the  number  of  teeth,  the  less  is  the 
room  taken  up  by  insulation. 

On  the  other  hand,  the  greater  the  number  of  coils  per  slot,  the 
greater  is  the  difference  between  the  position  of  the  slot  (with  respect 
to  the  pole-shoe)  when  the  first  coil  is  under  the  brush,  and  its 
position  when  the  last  coil  is  commuted.  Now,  this  difference  must 

Tiolf*    £l"Ff* 

not  be  too  great  (particularly  if  the  ratio  -^—    — r  is  small),  if  good 

IJO-LG  T/lLCil 

commutation  is  to  be  obtained.  So  that  a  practical  limit  to  the  coils 
per  slot  is  set,  and  this  varies  between  one  and  ten.  This  question 
must  be  discussed  more  fully  under  the  heading  of  Commutation,  but 
a  compromise  of  this  nature  can  only  be  determined  by  practice, 
so  that  an  empirical  rule  for  the  number  of  slots  for  estimating  pur- 
poses will  not  be  out  of  place  here.  Generally  speaking,  a  good  first 
approximation  is  arrived  at  by  making — 

The  number  of  slots  equal  to  four  times  the  armature  diameter  in 
inches. 

Another  consideration  affecting  the  number  of  slots  slightly  is  the 
type  of  winding  adopted.  This  will  be  more  particularly  dealt  with 
under  "  Armature  Windings  "  (Chap.  VIII.). 

Dimensions  of  the  Armature  below  the  Teeth. — In  small 
machines  a  density  as  high  as  95,000  lines  per  square  inch  may  be 
used,  and  this  determines  the  size  of  stamping.  In  large  machines, 
the  depth  of  the  stamping  is  ruled  very  often  by  considerations  quite 
apart  from  magnetic  density. 

For  if  calculated  for  a  density  as  high  as  100,000  in  a  slow- 
speed  machine,  the  stampings  would  be  mechanically  too  weak. 
Further,  necessity  for  ample  internal  ventilation  will  often  dictate 
the  best  density,  and  the  question  of  permissible  iron  loss  affects  the 
matter  to  some  extent  (see  p.  221). 

Eecently,  some  new  magnetic  materials  combining  high  per- 
meability with  low  iron-loss  have  been  brought  into  the  market.  Of 
these  the  best  known  is  "  stalloy,"  whose  curve  is  given  plotted  with 
that  of  "  lohys  "  (an  excellent  soft  iron  for  armature  sheets)  in  Fig.  14. 
The  comparative  iron-losses  for  plates  0'02"  thick  are  shown  in  Fig. 
16,  and  the  actual  iron-losses  for  stalloy  in  Fig.  15. 

It  is  a  curious  fact  that  for  continuous-current  machines  not  all 

*  See  Appendix  I. 


GENERAL  PROPORTIONS  OF  MODERN  MACHINES    17 

the  apparent  advantage  of  stalloy  can  be  obtained.  The  reason  for 
this  is  not  known ;  yet  the  fact  is  sufficiently  marked  to  lead  makers 
to  adopt  stalloy  for  alternating-current  apparatus,  and  to  adhere  to 
brands  such  as  lohys  for  direct-current  machines. 


Apart  from  these  modifying  factors,  the  density  aimed  at  below  the 
armature-teeth  should  be  about  80,000  lines  per  square  inch. 

Once  having  fixed  the  flux  per  pole  N,  then  all  the  main  dimen- 
sions of  the  machine  are  practically  determined. 

c 


1 8      CONTINUOUS   CURRENT  MACHINE   DESIGN 

N 


For  the  area  of  cast-iron  yoke  = 


about 


5-0 


4-0 


2-0 


1-0 


Area  of  pole  =  iWo  about 

(dia.  pole)2 

4 
or  for  square  poles  =  (pole  side)2 

Area  of  shoe  =  ^^  =  (  *? al  len^h  of 
54,000       (  shoe  X  pole-arc. 


7 


y 


0  10  20  30  40  50  60  70  80  90  100 

FREQUENCY  (CYCLES  PEU  SECOND). 

FIG.  15. — STALLOY  HYSTERESIS  AND  EDDY-CURRENT  LOSSES  FOR  VARIOUS 
DENSITIES  IN  LINES  PER  SQUARE  INCH. 


GENERAL  PROPORTIONS  OF  MODERN  MACHINES    19 


*  —f\  T*P 


—f 

And  since  -^  -  r—  r-  =  0'7  generally,  and  the  axial  length  of  the  shoe 
cannot  differ  greatly  from  the  pole-diameter  or  pole-side,  we  get  — 

N     =  ,  pole-diameter  or|x      le    itch  x  07> 
54,000       (  pole-side  J 


1 

1-5 
I 

£ 

£ 

1  1 

- 

0  $                               -rtr' 

"Yciuoui  \\  . 

O  •  OjL  wtfc     H^icfc.,  ^O  ^ 

> 

u 

1 

^ 

1 

/ 

- 

_. 

^ 

1 

1 

1 

j 

- 

1 

/ 

^ 

- 

/ 

2 

,/ 

2 

/ 

/ 

/ 

7 

1 

^ 

J 

/ 

y 

V 

1  / 

F 

V 

« 

h/ 

]f 

,  / 

o 

^ 

»f 

/ 

^ 

>/ 

/ 

/ 

/ 

2 

/ 

^ 

s 

- 

/ 

/ 

/ 

/ 

7 

j 

j 

' 

7 

2 

/ 

X 

x 

x 

I 

if                   25                     50                     75                     100 

KILO-LINES  PER  SQUARE  INCH. 
FIG.  16. 

The  art  of  designing  then  resolves  itself  into  adapting  the  most 
economical  Aux  to  the  greatest  number  of  conductors  on  the 

armature. 

Relationship  between  Field  and  Armature  Dimensions. — 
We  have  seen  that  the  most  generally  economical  field  for  machines 
under  100  K.W.  is  one  with  a  round  pole,  although  a  square  pole 
will  work  out  well.  It  is  often  difficult  to  decide  the  number  of 
poles  for  a  given  output ;  but  leaving  for  the  moment  the  number  of 


20      CONTINUOUS   CURRENT   MACHINE   DESIGN 

poles  per  K.W.,  an  important  relationship  may  be  established 
between  the  number  of  poles  of  given  diameter,  and  the  diameter 
of  the  armature.  The  length  of  armature  will  be  approx.  =  diameter 
of  pole,  but  it  may  be  a  little  longer,  to  leave  a  ledge  for  the  support 
of  the  field-coil. 

Pole-pitch  =  - 

Pole-arc  =  —  X  07  (allowing  ratio    P?le"?!Cu  =  07) 
p  pole-pitch 

.-.  area  of  pole-shoe  =  L  x  —  x  07 

P 

The  density  at  the  pole-face  must  lie  somewhere  between  50,000  and 
60,000  per  square  inch,  taking  54,000  as  a  first  approximation. 

Total  flux  per  pole  =L  X  —  -  x  07  x  54,000 

,.      ,         frd? 
Area  of  pole  =  — r 
4 

Flux  per  pole  =  ^  x  105  |(takin-  10.5  a?  the  tf 
4  I     per  sq.  inch  in  pole) 


Then  ^  x  105  =  L--  x  07  X  54,000  X  X 
4  p 


Whence  we  find  that  D  =  approx.  -^-^d 

1*  5A. 

giving  a  rough  figure  with  which  we  can  start  a  design. 

We  also  know  that  the  depth  of  slot  =  0'04D  on  the  assumption 

that  tooth-root  density  =  Wj>  and  that  the  width  °f  toP  °f  tooth  = 
width  of  slot. 

In  any  case,  assuming  that  there  is  a  maximum  tooth-root  density, 
then,  inserting  that  limit,  we  arrive  at  a  depth  of  slot  which  is 
entirely  independent  of  the  number  of  slots  used ; — a  point  of  great 
importance. 

On  the  other  hand,  if  a  square  pole  be  adopted,  we  have — 

d*  x  105  =  L  x—  X  07  x  54,000  x  X 
P 

D  =  rfxL' or  rlx^  - 

if  d  be  called  the  length  of  side  of  the  pole. 

It  may  also  be  pointed  out  that  if  the  flux  in  any  part  of  a 
machine  is  once  determined,  the  whole  proportions  of  the  magnetic 

*  For  meaning  of  symbols,  see  list  at  the  beginning  of  the  book. 


GENERAL  PROPORTIONS  OF  MODERN  MACHINES    21 


circuit  follow  as  a  matter  of  course  if  the  material  used  is  known. 
Thus  we  may  make  a  table  of  relative  areas  of  the  parts  of  the 
magnetic  circuit. 

TABLE  I. 


Part. 

Flux  density. 

Relative  area. 

Pole  face    . 
Pole. 
Yoke  —  cast  steel 
Yoke  —  cast  iron 
Teeth 
Armature  below  teeth 

Per  square  inch. 

50,000 
100,000 
80,000 
30,000 
120,000  to  150,000 
50,000  to  90,000 

2 

*    ! 

Wf)*A 
(I  to  I)*  A 

Where  A  is  the  Hopkinson  leakage  factor. 

General  Relationship  between  Output  and  Dimensions. — 

The  output  which  can  be  obtained  from  a  frame  proportioned  accord- 
ing to  the  rules  expressed  in  Chaps.  I.  and  II.,  depends  chiefly  upon 
two  considerations,  which  as  largely  influencing  also  the  relative 
proportions  of  the  various  parts  of  the  machine,  must  be  discussed 
before  turning  to  the  general  question. 

The  two  considerations  referred  to  are,  (1)  Temperature  rise,  (2) 
Commutation  or  sparking  limit. 

Now  the  E.M.F.  equation  for  a  generator  may  be  expressed  as 
follows  : — 


,r  ,,        revolutions  per  minute 
Volts  =  — — - — ~- 


poles 


v>      A 


60  "  armature  circuits 

total  armature  conductors  X  flux  per  pole 


If  both  sides  of  this  equation  be  multiplied  by  the  total  current 

we  get  — 

Watts  =  (poles  x  flux  per  pole)  x  (conductors  X  current  per 
conductor)  X  1Q8  *  6Q  .  *  ft-T.M  • 

(Poles  x  flux  per  pole)  is  sometimes  called  the  total  magnetic 
armature  loading,  and  is  denoted  by  Y.* 

(Conductors  x  current  per  conductor)  is  sometimes  called  the 
total  electric  loading  of  the  armature,  and  is  denoted  by  X.* 

*  Compare  Macfarlane  and  Burge,  Journal  I.E.E.,  vol.  XLIL,  p.  238. 


22      CONTINUOUS   CURRENT   MACHINE   DESIGN 

^      watts  output  XY 

Thus  =  8Peclfic  tor1ue  = 


B.P.M. 

T"iol  P»flT*P 

Now  poles  x  lines  per  pole  =  ?r  X  D  X  •**  -  —  -  x  axial-length 

of  pole-face  X  density  at  pole-face  ;  and  — 

armature-conductors  x  current  per  conductor 

=  -n-D  x  ampere-conductors  per  inch  (of  armature  periphery). 

Substituting  these  we  get  the  relationship  — 
D2  X  axial  length  of  pole-face 

=  _  60-8  x  107  X  pole-pitch  _       watts 
density  at  pole-face  X  amp.  condrs.  per  in.  x  pole-arc      E.P.M. 

If  we  now  put  in  the  average  values  for  these  quantities,  which 
cannot  change  much,  as  for  instance  — 

Density  at  pole-face,  say,  54,000  lines  per  square  inch. 
Eatio  pole-arc  -f-  pole  pitch,  say,  0*7. 

Then  D2  X  L  X  ampere-conductors  per  inch  =  16000  x  ,7^1 

K.r.M, 

If  we  adopt  poles  of  circular  section,  it  has  been  already  shown, 
with  the  foregoing  constants,  and  assuming  the  length  of  pole-face  = 
d,  that— 

^        p     ,          ,      1-5XD 
D  =  r£r  d,    or  d  =  - 
* 


.     ,       10,700  watts 
Hence  —  *  x  ampere-conductors  per  inch  = 


,  13,370  watts 

or  for  square  poles  =  —  V—  g-p-jj- 

The  importance  of  the  value  of  the  ampere-conductors  per  inch  (q) 
is  here  rendered  very  clear,  but  as  the  controlling  factors  —  heating 
and  commutation  —  both  depend  upon  it,  it  cannot  be  rigidly  fixed. 

For  small  machines  in  modern  practice  it  varies  between  very 
wide  limits,  but  for  large  machines  (over  500  watts  per  rev.  per  min.) 
it  has  an  almost  constant  value.  Indeed,  it  only  varies  between  700 
and  950,  so  that  if  we  insert  a  mean  value  of  800  in  the  formulae  we 
have  for  large  machines  the  extremely  useful  relationship  — 

watts 


E.P.M. 

Of  course  the  above  constants  are  empirical  to  this  extent,  that 
they  are  deduced  from  values  found  in  modern  practice  to  give 
satisfactory  results  in  the  case  of  machines  subject  to  limitations 
under  the  two  headings  "  commutation  "  and  "  heating."  They  cannot, 
therefore,  represent  the  best  that  can  be  done  with  interpoles,  nor 


GENERAL  PROPORTIONS  OF  MODERN  MACHINES    23 

should  they  be  used  in  any  case  for  other  than  obtaining  preliminary 
dimensions  or  for  checking  final  calculations. 

An  example  of  the  use  of  the  above  will  make  these  limitations 
clear.  Suppose  we  wish  to  design  a  200  K.W.  500  volt  machine  to 
run  at  400  E.P.M. 


-  Then  D*L  =  20  -=  10,000 

Now,  with  circular  poles  — 

D=    *    ,*=    *    L 

1  OA  1  OA 

.*.  for  4  poles,  L  =  |DX 
6  poles,  L  =  iDX 

And  the  machine  will  probably  have  either  4  or  6  poles. 

If  4  poles,  D3X  =  26,700 

D  =  nearly  29"  (X  =  1'15) 
D2L  =  10,000,  L  =  12" 

If  6  poles,  D3X  =  40,000 

D  =  about  33" 
L  =  9"  practically 

Now,  it  is  evident  that  D2L  is  a  measure  of  the  armature  volume, 
and  in  these  two  cases  the  value  is  about  the  same.  There  will, 
however,  be  differences  in  the  two  machines  in  the  following 
respects  :  — 

(1)  Peripheral  speed. 

(2)  Division  of  losses,  for  in  the  six-pole  machine  the  iron  loss 
will  be  greater  and  the  armature  copper  loss  probably  less. 

(3)  Surface  available  for  radiation  of  heat  slightly  different. 

(4)  Total  field  ampere-turns,  which  will  be  greater  in  the  six- 
pole  machine,  since  the  air-gap  length  and  densities  remain  about 
the  same. 

(5)  Eatio  armature  ampere-turns  to  field  ampere-turns. 

(6)  Size  of  field-frame. 

Therefore  before  we  can  even  decide  as  to  the  number  of  poles  or 
the  shape  of  the  machine  all  the  above  questions  must  be  examined. 
We  may  add  here  that  in  the  case  of  small  machines  not  even  an 
approximation  like  the  above  can  be  obtained.  For  neither  the  value 
of  the  ampere-turns  per  inch  nor  of  the  magnetic  densities  is  even 
approximately  constant,  so  that  other  methods  must  be  adopted. 

Now,  all  of  the  above  differences,  except  Nos.  (1)  and  (6),  affect  not 
only  the  actual  but  the  relative  proportions  of  the  armature  parts 
dealt  with  in  the  next  chapter.  The  size  of  field  frame  is  considered 
elsewhere,  but  the  peripheral  speed  question  may  be  dealt  with  here. 


24       CONTINUOUS   CURRENT   MACHINE   DESIGN 

Armature  Peripheral  Speed.— Except  in  the  case  of  Turbo- 
generators (which  are  not  here  considered)  the  armature  peripheral 
speed  has  never  been  a  serious  limiting  factor  in  dynamo  design.  On 
the  contrary,  economical  machines  usually  have  a  peripheral  speed 
which  does  not  exceed  4000  feet  per  minute.  Special  precautions 
would  have  to  be  adopted  if  this  figure  were  to  exceed  5000  feet 
per  minute,  but  there  is  no  necessity  for  the  use  of  such  a  high 
value. 

Commutator  Peripheral  Speed. — On  the  other  hand,  with  a 
peripheral  speed  of  commutator  exceeding  3500  feet  per  minute, 
chattering  of  the  brushes  and  consequent  difficulties  with  com- 
mutation are  always  likely  to  occur ;  and  this  figure  does  often  come 
in  as  a  very  real  limit  to  the  machine  dimensions. 


CHAPTER    III 

RELATIVE  PROPORTIONS  OF  THE 
ARMATURE  PARTS 

THE  proportioning  of  the  armature  is  affected  by  eight  considera- 
tions : — 

i.  Efficiency,  and  2,  division  of  losses  for  a  given  tempera- 
ture rise. 

3.  Pressure  and  current. 

4.  Standardization. 

5.  Appearance. 

6.  Ampere-turns  of  the  armature. 

7.  Commutation. 

8.  Use  of  Neutralization. 

i.  Efficiency,  and  2,  division  of  Losses  for  a  given  Tem- 
perature Rise. — If  the  efficiency  be  decided  upon,  the  proportion  of 
watts  lost  in  the  armature  to  those  lost  in  the  field  is  determined 
by  two  considerations,  viz. — 

(I.)  Efficiency  characteristic  required. 

(II.)  Whether  the  machine  is  to  be  sometimes  totally  enclosed. 
(I.)     Efficiency   Characteristic    required. — The    losses   of  a 
machine  may  be  practically  subdivided  into — 

(a)  Constant  Losses,  consisting  of  friction,  hysteresis,  and 
eddy-currents,  and  the  shunt-field  loss.     These  losses  are 
not  actually  but  are  practically  constant ;  and 
(&)  Variable  Losses,  consisting  of  armature  and  commutator 

C2E  loss,  and  series-field  loss. 

The  efficiency  of  a  machine  is  a  maximum  when  a  =  b.  Thus  the 
division  of  losses  determines  the  load  at  which  the  efficiency  is  a 
maximum.  The  choice  of  this  load  will  depend  upon  the  nature  of 
the  service  required.  Thus  a  dynamo  with  an  average  load  =  75  per 
cent,  of  its  full  load,  should  have  its  maximum  efficiency  at  this 
point,  and  so  on.  Figs.  18  and  19  show  average  values  of  the  com- 
mercial efficiency  of  standard  machines  at  full  load  ;  and  Fig.  17 
shows  the  variation  due  to  speed. 


26       CONTINUOUS 


NT   MACHINE   DESIGN 


At  the  point  of  maximum  electrical  efficiency,  the  preliminary 
division  of  losses  for  a  shunt^machine  is  determined  by 


(1)  E!  =  E 


1  - 


*(2)  E/  =  E  J-i-?.1 
1  —  »h 

where    EI  =  armature  commutator  and  series  field  resistance, 
E/  =  shunt-field  resistance  corresponding  to  the  load, 
and        ra  =  the  electrical  efficiency. 


87 


10 


70 


23456 

FIG.  17. — CURVE  BETWEEN 


SO 


7 
K.W. 

VR.P.M. 


90 


100 


110  Upper  Curve. 
K.W. 


V  R.P.M. 

10  Lower  Curve. 


AND  EFFICIENCY. 


Since,  however,  not  only  the  shunt  losses,  but  all  the  constant 

E2 
losses  may  be  included  in  an  expression  like  ^,  we  may  extend  the 

use  of  the  above  formulae  as  follows  : — 

Let   EI,  as  before,  be  the  resistance  of  the  various  paths  in  series 
carrying  current  (armature,  compound  winding,  and  commutator), 


*  See  Appendix  II, 


RELATIVE  PROPORTIONS  OF  ARMATURE  PARTS     27 

E2 

Let  E2  be  such  a  resistance  that   ~  —  the  sum  of  all  the  constant 

±i2 

losses,  where  E  is  the  approximately  constant  terminal  potential 
difference. 

Let  E  be,  as  before,  the  external  resistance  corresponding  to  the  load 
at  which  the  commercial  efficiency  (17)  is  to  be  a  maximum. 


91 


90 


88 


8fl 


200 

10 


400 
30 


600 
50 


800 
70 


1000  Upper  Curve. 
90    Lower  Curve. 


A — Exceptionally  Low  Speed. 
B— Exceptionally  High  Efficiency. 


FIG.  18. — CURVE  BETWEEN  K.W.  AND  EFFICIENCY. 


Then 


.  _  p  1  - "2 

11     It      — -7 

>12  =  E  1±3 


for  maximum  efficiency. 

E2 
Now,  of  the  various  components  into  which  ^  is  divisible,  we  can 

predetermine  with  considerable  accuracy  the  commutator  friction  and 
the  iron  loss.  The  other  friction  losses  vary  usually  from  0'5  per 
cent,  in  large  machines  to  2  per  cent,  of  the  output  in  small  machines, 

E2 

and  the  balance  of  ^-  is  the  shunt-field  loss. 


28       CONTINUOUS   CURRENT   MACHINE   DESIGN 

These  equations  are  only  occasionally  useful,  since  usually  it  is 

E2 
not  the  actual  value  E2  that  is  needed,  but  only  p- .    Consequently, 

more  often  the  method  illustrated  in  the  following  paragraph  is  of  use. 


100 


20 


40  60 

OUTPUT  B.H.P. 


so 


100 


(1)  Full-load  Efficiency  Curves  of  Shunt  and  Compound  Motors. 

(2)  Full-load  Efficiencies  of  Series  Motors,  including  Single  Gearing. 

FIG.  19. 

Allotment  ot  Constant  Losses. — Suppose  the  commercial 
efficiency  of  a  200  K.W.,  500  volt,  400  K.P.M.  generator  to  have  a 
maximum  value  of  93  per  cent,  at  three-quarter  full  load. 

Then  constant  losses  and  variable  losses  at  f  full  load  =  7  per  cent. 

=  10-5  K.W. 

And  constant  losses  =  variable  losses  =  5*25  K.W.  at 

this  load. 

If  we  have  an  idea  of  the  armature  diameter  and  length  (from 
such  a  preliminary  equation,  for  instance,  as  that  developed  in  the 
last  chapter),  then  we  also  have  an  approximation  to  the  size  of  the 
pole.  Erom  Table  I.  p.  21,  we  obtain  the  approximate  section  of 
the  armature  below  the  teeth,  the  depth  of  which  may  be  roughly 
estimated.  Then  we  have  sufficient  particulars  for  the  iron  losses,  as 
will  presently  be  seen  ;  and  from  Chapter  IX.  p.  133,  the  commutator 
loss  can  be  closely  estimated.  Thus  we  have  to  a  first  approximation 
not  only  the  actual  losses,  but  also  the  way  in  which  they  are  to 
be  allotted. 


RELATIVE  PROPORTIONS  OF  ARMATURE  PARTS    29 

Applying  the  above  as  far  as  we  are  yet  able,  it  has  been  shown 
that  the  armature  diameter  and  length  for  a  four-pole  machine  would 
be  29"  and  12"  respectively  (p.  23).  Taking  depth  of  slot,  say  about 
0-05D  or  1-5",  we  have— 

TABLE  II. 

Diameter  at  tooth  root  =26" 
Pole  diameter  =  12" 

Pole  area  =  113  sq." 
Ratio  of  relative  areas,  say  =  J 

Armature  area  below  teeth  =  70  sq."  nearly  (=  |  x  113) 
Armature  nett  length,  say  =  10"  (=  12"  X  0-83) 

radial  depth        =  7" 
and  internal  diameter  =  12"     1 

mean  diameter  =12  +  8*5  =^20'5" 

Vol.  armature,  neglecting  slots  =  7rX20'5x8-'5  x  10  =  5500cub.in. 
Weight  in  Ibs.  =  5500  x  0'28  =  1540 

v  2  x  400  .    1Q1 

Frequency  =  — -^—  =  13J 

Approx.  density  =  60,000  lines  per  sq.  in. 

In  a  similar  way  the  weight  of  the  teeth  can  be  calculated,  and 
we  need  a  method  of  determining  the  watts  per  Ib.  of  iron  in  terms 
of  the  density  and  frequency.  For  "  Stalloy  "  such  curves  have  already 
been  given.  For  ordinary  armature  iron  we  may  obtain  an  exceed- 
ingly good  approximation  from  a  general  formula  as  developed  below. 
It  is,  however,  again  worth  while  calling  attention  to  the  fact  that 
no  approximations  are  very  accurate  for  very  small  machines. 

Estimation  of  Iron-loss. — It  will  be  seen  that  in  any  case  the 
predetermination  of  hysteresis  and  eddy  losses  is  an  important  item 
in  the  design  of  continuous-current  generators.  Theoretical  formulas 
for  this  loss  are  very  unsatisfactory  and  almost  always  lead  to  much 
too  small  a  result.  Careful  experiments  upon  toothed  core  discs 
clamped  together  and  running  in  a  carefully  measured  field,  yield  the 
following  formulae,  which  can  be  used  for  estimating  the  loss  :— 

Iron-loss  in  watts  per  Ib.  =  ~  per  sec.  x  millions  of  lines 

per  sq.  in.  x  constant. 

The  constant  here  varies  to  some  extent  with  the  manner  in  which 
the  volume  of  the  armature  is  calculated  in  the  test  cases.  If  the 
tooth  densities  are  not  exceptional,  and  the  armature  is  treated  as 
a  cylinder  having  an  outside  diameter  =  D  and  an  inner  dia- 
meter =  the  actual  inner  diameter  of  the  discs,  with  a  length  =  nett 
length  of  the  stampings ;  if,  moreover  the  density  in  this  calculation 
is  taken  as  the  average  value  below  the  teeth,  and  the  discs  are  not 


30      CONTINUOUS   CURRENT   MACHINE   DESIGN 

more  than  0'02"  thick; — then  the  constant  varies  in  the  author's 
experience  between  1*7  and  1*9,  and  can  easily  be  deduced  from 
consistent  tests  on  any  given  type  of  machine.  With  fair  lamination 
1*8  is  a  good  value. 

The  theoretical  formulae  are  as  follows : — 

Hysteresis  loss  in  watts  per  cubic  inch  =  frequency  X  (density)1'6 

X  10~7  X  hysteretic  constant 

This  hysteretic  constant  varies  with  the  quality  of  the  iron  from 
about  G'0016  in  first-rate  material  to  0*0032  in  low-grade  iron. 

Eddy-current  loss  in  watts  per  cubic  inch  =  150  X  (frequency)2 

X  (density)2  X  (thickness  of  plate)2  X  10~12 

The  frequency  in  the  above  formulae  is  in  cycles  per  second,  the 
density  is  in  lines  per  square  inch,  and  the  thickness  of  plate  in 
inches.  Sometimes  these  formulas  will  give  a  fair  approximation  to 
the  loss,  especially  when  the  lamination  is  very  carefully  carried  out, 
all  burrs  being  avoided.  They  are  especially  useful  for  checking 
purposes,  particularly  when  any  of  the  densities  used  are  abnormal ; 
for  the  loss  in  any  part  (e.g.  the  teeth)  can  be  separated  from  the 
rest  of  the  losses.* 

Of  course,  with  any  well-known  brand  of  iron  a  series  of  curves 
like  those  in  Fig.  16  can  be  used  instead  of  the  above  formulae. 

Continuing  the  example  on  p.  29,  and  taking  1/9  as  the  constant 
in  the  iron  loss  formula,  we  get — 

Iron  loss  per  Ib.  =  13 1  x  0'06  X  1/9  =  1/5  watts 
Approximate  loss  =  1*5  X  1540  =  2350  watts 

If  the  friction  loss  be  0'6  per  cent.,  i.e.  1200  watts,  we  have 
5250  —  3550  =  1700  for  shunt-field  and  commutator  friction  losses. 

The  above  illustration  shows  the  effect  of  the  losses  on  the 
efficiency  curve.  It  would  naturally  be  easier  to  design  so  that  the 
full  load  efficiency  is  about  a  maximum,  and  this  is  more  usually 
done,  as  will  be  illustrated  in  subsequent  examples. 

After  subdivision  of  the  constant  losses  as  above,  or  in  cases  where 
such  allotment  is  difficult,  the  curve  Fig.  20  (whose  shaded  portion 
shows  the  ordinary  limits  of  field  losses  in  modern  machines)  may  be 
used  as  a  check  or  for  approximate  preliminary  calculation. 

Variable  Losses. — The  subdivision  of  the  variable  losses  may 
be  carried  out  as  follows  : — 

The  commutation  resistance  loss  is  at  once  determined  by  the 
commutator  design  (see  pp.  133,  135).  In  the  case  of  compound 
machines  the  armature  and  compound  resistance  losses  are  divided  in 
any  way  most  convenient.  Usually  the  compounding  is  arranged  to 
suit  a  standard  shunt  machine  of  definite  output.  Compounding 

*  See  footnote,  p.  204. 


RELATIVE  PROPORTIONS  OF  ARMATURE  PARTS    31 

then  reduces  the  shunt-field  loss,  increases  the  hysteresis  loss  (because 
higher  saturations  are  reached),  and  transfers  the  balance  of  the 
constant  losses  as  a  variable  loss  to  the  field. 

Series  machines  (usually  traction,  lift  or  crane,  motors)  are 
designed  from  an  entirely  different  point  of  view,  which  will  be 
considered  later,  but  the  values  of  their  ordinary  efficiencies  have 
already  been  given  in  Fig.  19. 


\  40  60 

OUTPUT  IN  KW. 

FIG.  20. — CURVE  OP  SHUNT  FIELD  Loss. 


100 


(II.)  Effect  of  Enclosing. — When  a  standard  open-type  machine 
is  enclosed,  the  losses  (and  therefore  the  output)  have  to  be  lowered 
to  keep  the  temperature-rise  within  reasonable  limits.  Eeducing  the 
output,  however,  practically  only  changes  the  variable  losses ;  so  that 
if  these  be  small  compared  to  the  others,  a  large  reduction  of  output 
only  results  in  a  small  reduction  of  temperature-rise.  Hence,  if  a 
machine  is  to  give  a  good  output  per  unit  of  weight  when  enclosed, 
the  constant  losses  must  be  kept  down.  This  is  often  the  chief 
determining  factor  for  the  division  of  losses  in  small  motors.  The 
following  may  be  taken  as  modern  representative  figures : — 

The  ratio  variable  losses  :  constant  losses  varies  from  1  :  2  for  a 
small  5  B.H.P.  machine  to  2'5  :  1  for  a  machine  of  100  B.H.P.  output. 

The  reason  for  this  large  variation  is  evident  when  it  is  recollected 
that  whereas  the  smaller  machine  may  require  about  4000  ampere- 
turns  on  each  pole  of  its  field,  the  larger  machine  only  requires 


32      CONTINUOUS  CURRENT   MACHINE  DESIGN 

about  8000  ampere-turns,  an  increase  not  comparable  with  its 
increased  output.  Thus  the  constant  field-loss  is  a  much  larger 
percentage  of  the  total  losses  in  the  case  of  the  smaller  machine 
than  it  is  in  the  case  of  the  larger  machine.  On  the  other  hand, 
machines  of  more  than  30  B.H.P.  rarely  are  required  totally  enclosed, 
and  if  they  were,  such  sizes  are  worth  while  designing  separately.  So 
that  this  argument  really  affects  small  machines  most,  in  which  the 
above  ratio  varies  at  best  from  J  at  5  B.H.P.  to  unity  at  30  B.H.P. 

Estimation  of  Copper  Loss. — In  drum-wound  armatures  the 
length  of  one  conductor  with  its  end-connection  is  nearly 

(armature  core  length  +  4*5— ) 
The  armature  copper  loss  is  then 

(current  per  conductor)2  X  (core  length  +  4*o_  )  x  p  x  w  _i_  section 

\  jp 

of  one  conductor 

In  this  formula  p  =  specific  resistance  of  copper  =  0*00000076 
ohms  per  inch  cube  at  50°  C. 

C 
In  multiple-circuit  armatures  the  current  per  conductor  =  -  (see 

Chap.  VIII.). 

C 
In     two-circuit    armatures    current    per    conductor  =  ^    (see 

Chap.  VIII.). 

Combining  the  formulae  for  copper  and  iron  losses,  we  can  find 
the  total  loss  to  be  dissipated  by  the  armature  as  heat.  But  the 
surface  from  which  this  heat  will  be  dissipated  is  extremely  difficult 
to  estimate,  and  may  be  taken  in  a  variety  of  ways. 

The  temperature-rise  then  depends  upon  the  peripheral  speed,  the 
ventilation,  and  the  number  of  watts  per  square  inch  to  be  dissipated. 
And  this  is  a  most  important  relationship  to  determine.  The  more 
so  since,  with  the  introduction  of  interpoles,  the  allowable  tempera- 
ture-rise becomes  almost  the  sole  factor  limiting  the  size.  A  special 
chapter  is  therefore  devoted  to  this  question. 

As  a  guide  or  check  in  the  matter  of  armature  (Fig.  21),  C2E  loss 
is  appended,  which  sets  out,  as  does  Fig.  20  for  field  losses,  the  usual 
range  of  armature-losses  in  practice. 

3.  Influence  of  Pressure  and  Current. — The  design  of  a 
machine  will  vary  greatly  according  as  it  is  intended  for  high  or 
for  low  pressure ;  comparing  two  machines  of  similar  output,  one  of 
which  is  capable  of  giving  100  amperes  at  400  volts,  and  the  other 
400  amperes  at  100  volts,  the  commutator  for  the  latter  will  require 
by  far  the  larger  surface,  both  for  radiation  and  collection,  to  give  the 


RELATIVE  PROPORTIONS  OF  ARMATURE  PARTS    33 

same  final  temperature-rise.  With  regard  to  the  armatures,  more 
space  will  be  taken  up  by  the  insulation  in  the  case  of  the  high 
voltage  machine.  Hence,  the  lower  the  current  the  shorter  the 
commutator,  and  the  higher  the  voltage  the  smaller  the  amount  of 
space  available  for  copper,  so  that  an  increase  in  the  armature  is 
necessitated  in  order  to  keep  the  same  temperature  rise.  Thus  it  is 
convenient  to  lengthen  the  armature  in  the  high  voltage  case.  (It 
would  be  possible  to  increase  the  diameter  of  the  armature  but  for 
the  fact  that  a  different  size  of  disc  for  every  different  voltage  would 
necessitate  keeping  a  very  large  number  of  standard  sizes  of  discs  in 


1    ' 


20 


40 


60 

OUTPUT  IN  K.w. 


80 


100 


FIG.  21.  —  CURVE  OF  C2R  Loss  IN  ABMATUKE. 

stock.)  The  amount  by  which  the  armature  is  lengthened  is  usually 
about  that  by  which  the  commutator  is  shortened.  In  small  machines 
this  adjusting  of  the  armature  and  commutator  rarely  pays.  It  is, 
indeed,  better  to  keep  the  armature  dimensions  fixed,  and  adjust 
the  output  or  the  speed,  or  to  leave  room  in  the  standard  frame 
for  the  largest  commutator  that  will  be  required.  It  will  pay  to 
shorten  the  commutator  for  the  higher  voltages,  and  the  frame 
must  be  designed  to  take  the  commutator  required  by  the  lowest 
voltage. 

4.  Standardization.  —  The  use  of  standard  parts  plays  a  very 

D 


34      CONTINUOUS   CURRENT   MACHINE   DESIGN 

important  role  in  large  works,  and  it  is  the  duty  of  the  designer  to 
see  that  the  number  of  standard  sizes  is  kept  as  low  as  possible. 

Whenever  the  output  of  a  machine  has  to  be  changed  by  any 
considerable  amount,  it  is  best  to  get  out  a  complete  new  series  of 
designs,  and  find  out  therefrom  the  most  economical  proportions ; 
having  adopted  these,  slight  changes  in  armature  length  will  give 
necessary  adjustment  for  current  and  voltage,  etc. 

5.  Appearance. — The  appearance  of  a  machine  is  not  always 
conducive  to  the  most  economical  design,  as  we  have  already  seen  in 
the  case  of  the  Lahmeyer  type  referred  to  on  p.  9. 

The  ratio  of  armature-diameter  to  armature-length  being  depen- 
dent upon  the  efficiency,  upon  the  number  of  poles,  and  upon  the 
cost,  we  not  infrequently  find  that  the  most  economical  shape  gives 
an  ugly  machine.  Fig.  22  is  an  example  of  such  a  case.  It 
represents  a  machine  very  economical  as  to  material  machinery  and 
performance,  but  very  difficult  to  sell  on  account  of  its  appearance. 
It  is  practically  impossible  to  make  a  machine  of  the  same  output  in 
the  round  type  so  economical  as  the  one  illustrated,  and  yet  such  a 
design  does  not  pay  as  compared  with  Fig.  23.  This  factor  of 
appearance  is  always  specially  important  in  the  case  of  small 
machines,  and  it  is  responsible  for  modifications  in  design  referred 
to  later. 

6.  Ampere  -  turns    of   the    Armature. — These    are    usually 
calculated  per  pole,  and  evidently  have  the  value — 

Ampere-turns  of  \  _  No.  of  conductors      current  per  conductor 
the  armature    /  ~  2  poles 

The  values  of  the  current  per  conductor  for  different  types  of 
winding  are  given  in  Chap.  VIII.,  and  it  is  impossible  to  discuss  the 
armature-strength  without  reference  to  the  field,  so  that  further 
consideration  of  this  point  is  reserved  for  Chap.  V. 

7.  Commutation. — There  is  a  limit  to  the  self-induction  of  a 
coil  undergoing  commutation  if  sparklessness  is  to  be  maintained 
during  the  process.     This  limit  is  discussed  under  the  heading  of 
"  Commutation,"  p.  128,  where  it  is  shown  that  the  actual  output  of 
the  machine  can  be  put  in  terms  of  the  turns  per  commutator  section, 
the  flux  per  pole,  and  the  speed.     Since  these  factors  have  a  bearing 
upon  the  armature  dimensions,  it  is  obvious  that  from  them  a  limiting 
expression  can  be  derived  as  is  done  on  pp.  131,  132. 

8.  Use  of  Neutralization.— If  by  means   of  "interpoles"  or 
" commutating  poles"  (see  pp.  54,  121)  the  armature  reactions  are 
reduced,  the  limit  of  output  is  changed,  temperature-rise  becomes  the 
chief  factor,  and  ventilation  of  the  utmost  importance.     By  such 
means  the  armature  ampere-turns  per  pole  may  be  greatly  increased, 
or  the  field-strength  per  pole  reduced ;  so  that  with  the  same  field 


FIG.  22. — OBSOLETE  BIPOLAK  MACHINE  (CRYPTO  ELECTRICAL  Co.). 


FIG.  23.— MODERN  BIPOLAR  MACHINE  (CRYPTO  ELECTRICAL  Co.). 

[To  face  p.  34. 


RELATIVE  PROPORTIONS  OF  ARMATURE  PARTS     35 

loss  much  less  copper  may  be  used.  It  is  found  in  practice  that  the 
cost  of  the  material  thus  saved  is  considerably  greater  than  the  extra 
cost  involved  in  fitting  commutating  poles,  especially  in  large 
machines,  so  that  commutating  poles  must  henceforth  form  an 
essential  part  of  large  continuous  current  machines.  For  it  must  be 
borne  in  mind  that  such  machines  are  limited  in  size,  not  only  by 
temperature-rise  but  also  by  commutation,  and,  further,  that  the 
latter  limit  has  been  forced  up  by  high  air-gap  and  tooth  densities. 
So  that  commutation  affects  the  cost  and  dimensions  more  than  is 
at  first  apparent ;  obviously  in  those  instances  where  commutation 
was  the  limit,  with  commutating  poles  the  output  may  be  raised  till 
temperature  steps  in,  and  then  again  it  may  be  carried  further  by 
lower  air-gap  densities  or  shorter  gaps,  as  is  evidenced  by  Fig.  13. 
The  saving  obtained  is  well  illustrated  by  the  comparison  carried 
out  on  pp.  189-196. 


CHAPTER   IV 

RELATIVE    PROPORTIONS    OF   THE    FIELD 
MAGNET  PARTS-FIELD  CALCULATION 

THE  main  proportions  of  the  field-magnet  are  (as  has  been  shown) 
dependent  upon  the  materials  used,  upon  economy  in  the  use  of 
those  materials,  and  upon  the  flux  per  pole.  There  is,  however,  an 
exceedingly  important  dimension  which  depends  upon  other  factors, 
viz.  the  length  of  the  magnetizing  bobbins  or  coils.  Kef erring  for  a 
moment  to  Figs.  41  and  44,  it  will  be  seen  that  the  coil  length  (lc), 
depends  upon  a  number  of  factors.  For  instance,  it  depends  upon 
the  position  of  the  compound  winding,  if  any  (Fig.  41) ;  and  upon 
the  use  and  shape  of  the  spool  or  bobbin  upon  which  the  wire  is 
wound.  But  more  than  either  of  these  it  depends  upon  the  ampere- 
turns  required  for  each  coil,  and  upon  the  temperature  rise  of  the 
coil  that  is  allowed  under  normal  working  conditions.  The  latter 
factor  is  discussed  in  the  chapter  on  temperature-rise ;  with  the 
former  we  shall  deal  now. 

On  p.  14  a  method  for  approximately  determining  the  field 
ampere-turns  per  pole  has  been  given.  For  final  calculations  of 
course  a  more  accurate  determination  is  necessary,  and  though  the 
reader  is  assumed  to  be  familiar  with  the  principles  of  these 
calculations,  we  must  work  out  a  simple  case  here  to  render  sub- 
sequent corrections  quite  clear. 

Fig.  24  gives  a  dimensioned  sketch  of  part  of  the  field  and 
armature  of  a  multipolar  machine.  The  path  of  the  flux  is  from  the 
pole  F  along  the  yoke  C  through  the  pole  G,  across  the  gap  and 
teeth,  and  return  by  the  armature-teeth  and  gap  to  the  pole  F.  In 
parallel  with  the  yoke  C  and  armature  D  is  a  second  path  for  the 
flux  passing  through  the  pole  G,  viz.  via  armature  and  yoke  H  and  the 
next  pole  to  the  left  (see  Fig.  25).  This,  however,  need  not  confuse 
the  calculations,  since  it  is  clearly  the  business  of  the  magnetizing  coil 
around  the  pole  G,  to  maintain  such  a  magnetic  potential-difference 
as  will  carry  the  flux  through  the  required  path  from  C,  via  pole  G 


FIELD-MAGNET    CALCULATIONS 


37 


and  gap  to  the  point  D ;  and  if  it  maintain  this  magnetic  potential- 
difference  on  the  one  side,  it  will  also  maintain  it  on  the  other,  i.e. 
towards  H,  since  the  two  paths  are  in  parallel.  Thus  each  coil  may 
be  considered  as  responsible  for  such  a  part  of  the  paths  as  that  lying 
between  the  points  C  and  D. 

Let  Ay  be  the  sectional  area  of  the  yoke  perpendicular  to  the  lines 

of  force. 

Ap  be  the  sectional  area  of  the  pole  do.  do. 

Ag         „  „  „         gap  do.  do. 

At         „  „  „        teeth  do.  do. 

Aa        „  „  „         armature  below  the  teeth. 

Let  J3y  fip,  etc.,  represent  the  magnetic  densities  in  the  sections 


FIG.  24.— EXAMPLE  OF  A  MAGNETIC  CURRENT. 

Ay,  Ap,  etc.,  and  let  the  materials  of  which  the  circuit  is  composed 

be  as  follows  : — 

Yoke  .  .  .  .  .  cast  iron 
Poles  .  .  .  .  .  cast  steel 
Armature  .  .  .  ,  .  lohys  iron 

The  necessary  dimensions  will  be  found  in  Fig.  24,  or  in  the  details 
below : — 

Slot  depth,  1-3"  Number  of  slots,  96 

Slot  width,  0-3"  Yoke  width  parallel  to  shaft,  18" 

Air-gap  length,  J"  Flux  per  pole  =  10  x  10°  lines 

1.  Ay  =  6"  x  18"  =  108  square  inches. 


38      CONTINUOUS   CURRENT   MACHINE   DESIGN 


Since  the  flux  divides  through  the  yoke,  half  going  either  way 

10  x  106 


108  x  2 


=  43,100 


From  Fig.  6  the  ampere- turns  per   inch  corresponding   to   this 
density  and  this  material  are  100. 

Therefore  ampere-turns  required  for  the  yoke  =  100  x  16  =  1600. 

2.  Ap  =  TT  x =  113  sq.  ins. 


4 

10  X  106 
113 


=  88,500 


The  ampere- turns  per  inch  corresponding  to  this  material  and 

density  are  about  30  (Fig.  6). 

Therefore  ampere- turns  re- 
quired for  the  pole  =  30  x  8" 
=  240. 

3.  Ag.  The  area  of  the  gap 
may  be,  in  the  first  instance, 
estimated  as  the  mean  area  of 
the  pole-face  and  of  the  tops  of 
the  teeth. 

Now,  area  pole-face  =  13" 
X  14"  =  182  square  inches. 

Number  of  teeth  under  one 
pole-face  =  16*8. 

If  85  per  cent,  of  the  arma- 
ture axial  core-length  be  the 
nett  length,  i.e.  be  iron  (the  rest 
being  ventilation  spaces  and 
insulation  between  laminae),  we 
have — 

Axial  length  of  one  tooth  =  0*85  x  14  =  12"  nearly 
Width  of  tooth  at  armature-face  =  0-485" 

^8  X  0485  x  12  =  97-5  s,.  in, 

97-5  4.  182 
Mean  gap  area  =  -    — s~~  ~  =  1397  sq.  ins. 

fig  =  7200  0 
Ampere-turns  for  gap  =  0-313  X  7200Cx  f  =  5650 

4.  At.  This  may  be  taken  as  the  mean  between  the  tooth  area 
at  the  armature  face  and  that  at  the  tooth  root.  The  section  at  the 
armature  face  has  already  been  calculated  as  97 '5  sq.  inches. 


FIG.  25. — MAGNETIC-CIRCUITS  IN  A 
MULTIPOLAK  MACHINE. 


FIELD-MAGNET   CALCULATIONS  39 

he  width  of  the  tooth  at  the  root  is  =  slot-pitch  at  tooth-root  - 
width  of  slot. 

=  (TT  X  dia.  at  bottom  of  teeth  -7-  No.  of  teeth)  —  width  of  slot 


Area  of  teeth  )  ,  width  at  root 

,  \  =  area  of  teeth  at  armature  face  x  —  .  -TTT—  r-£— 
at  tooth-root  J  width  at  face 

=  97-5  x  =  80  sq.  ins. 


=  =  887  sq.  ins. 

a 


Ampere-turns  for  teeth  per  inch  (from,  say,  Fig.  27)  =  120 

Ampere-turns  for  teeth  =  120  x  1'3" 

=  156 
5.  Aa. 
Area  of  the  armature  iron  below  teeth  =  Aa 

=  nett  axial  length  of  armature  X  radial  depth 
=  12  x  6 
=  72  sq.  ins. 

Here  again  the  flux  per  pole  divides,  half  going  either  way. 
^  =  ^,70,000. 

Corresponding  to  ampere-turns  per  inch  =  10 

ampere-  turns  for  armature  =  10  x  7" 

=  70 

So  total  ampere-turns  required  to  be  provided  by  the  field  coil 

=  1600  +  240  +  5650  +  156  +  70 
=  7716  per  pole 

Note  here,  as  nearly  always,  that  the  ampere-turns  required  for  the 
armature  iron  are  negligible. 

Corrections  to  the  above  Calculation.  —  1.  Effective  area  of  the 
air-gap.  This  has  been  taken  as  the  average  of  pole-face  and  tooth- 
tops,  i.e.  it  is  assumed  that  the  flux  is  evenly  distributed  along  the 
pole-face,  stopping  suddenly  at  the  pole  edges  ;  and  that  it  passes 
across  the  gap  straight  into  the  tops  of  the  teeth  only.  Neither 
assumption  is  correct.  From  the  edges  of  the  pole-shoes  a  so-called 
"  fringing  "  takes  place,  and  the  allowance  for  this  fringing  increases 
the  area  of  the  pole-  face  by  an  amount  which  by  some  writers  is 
taken  into  consideration  by  adding  one  or  two  teeth  to  those  actually 


40       CONTINUOUS   CURRENT   MACHINE   DESIGN 

under  the  pole-face ;  others  add  10  per  cent,  to  the  area  calculated 
in  the  example.  More  correctly  it  may  be  considered  by  taking  the 
pole-arc  as — 

Pole-arc  +  gap-length  x  constant 

This  constant  depends  chiefly  upon  the  ratio — 
distance  between  pole-shoes 

length  of  air-gap 

and  values  are  given  for  it  in  the  following  table  due  to  F.  W. 
Carter:—* 

TABLE  III. 


Distance  between! 

pole  -  shoes  ~-  y 
length  of  gap  J 

4 

5 

6 

7 

8 

9 

10 

12 

14 

16 

18 

Constant      . 

1-32 

1-59 

1-79 

1-98 

2-15 

2-3 

2-43 

2-65 

2-84 

3 

3-15 

Distance  between! 

pole  -  shoes  -f-  > 
length  of  gap  J 

20 

22 

24 

26 

28 

30 

35 

40 

45 
4-28 

50 

60 

Constant. 

3-28 

3-4 

3-51 

3-61 

3-7 

3-78 

3-98 

4-14 

4-4 

4-66 

Example  of  Corrected  Pole-arc. — Thus,  according  to  this 
correction  our  air-gap  area,  not  considering  the  slots,  would  be 
calculated  as  follows  : — 

Distance  between  pole-tips  =  TT  X  24*5      .,  Q       ^n 

~T~ 

, .    distance  between  pole-tips        7 

ratio = -£- £-  =  7r-?~  =  28 

gap-length  0*25 

constant  =  3'7 
effective  pole-arc  =  13"  +  3'7  x  0*25 

=  13-926" 
effective  pole-arc  area  =  13'926  x  14" 

=  195-59  instead  of  182  sq.  ins. 

Effect  of  Slots. — F.  W.  Carter  has  also  deduced  a  mathematical 
expression  for  the  effect  of  the  slots  upon  the  area  of  the  gap. 
According  to  his  correction,  the  air-gap  density  is  calculated  upon 
the  assumption  of  no  slots  existing,  and  this  is  then  multiplied 

*  Journ.  Inst.  Elec.  Eng.,  vol.  29,  p.  436. 


FIELD-MAGNET   CALCULATIONS  41 

by  a  constant  which  is  to  be  taken  from  the  curves  Fig.  26.  It 
will  be  seen  that  the  value  of  the  constant  depends  upon  the  value 
of  the  slot- width,  gap-length,  and  tooth- width. 

Applying  this  again  to  the  case  under  discussion,  we  should  have — 


Density  in  air-gap  if  there  were  no  slots  = 
tooth-width 


10  X  106 
195 


51,300 


ratio 


slot- width 


96 
0-485 
0-3 
0-3 


=  1-61 


, .     slot -width  _ 
gap -length  ~~  0'25 


=  1-2 


l-G 


1-4 


1-3 


1-2 


1-1 


1-0 


K 


0-9 
1-0 
1-1 

1-2 
1-3 
1-4 
1-5 

1-7 


2-r. 


3-5 
4 


10 


a  =  Breadth  of  Tooth. 
6  =  Breadth  of  Slot. 
g  —  Length  of  Air-Gap. 

FIG.  26. — EQUIVALENT  AIR-GAP. 


Constant  from  Fig.  26  =  T075  approx. 

Actual  air-gap  density  =  51,300  x  T075  =  52,500  (as  against  72,000) 
Corrected  ampere-turns  for  the  gap  =  0'313  x  52,500   x  0'25 

=  4140 


42       CONTINUOUS   CURRENT   MACHINE   DESIGN 

As  against  the  5650  previously  calculated,  making  a  total  of  6206,* 
instead  of  7716  ampere-turns  per  pole.  Thus  the  rough  calculations 
are  open  to  grave  errors,  and,  though  useful  for  preliminary  trial 
designs,  should  always  be  checked  by  a  closer  calculation.  In  the 
same  way  (as  has  also  been  pointed  out  by  Carter)  the  correction 
for  ventilating  spaces  in  the  centre  of  an  armature  may  be  allowed 
for.  Thus  if  in  the  present  instance  there  were  two  half-inch  air 
spaces  in  the  armature  core,  the  relationship  of  the  width  of  these  to 
half  the  remainder  of  the  core  would  be  similar  to  that  existing 
between  a  slot  and  a  tooth ;  we  might  say 

ratio  =  ^  :  0-5  =  8-6  :  1 

a.         ,     slot       0'5 
Since  also  -  -  =  :— ~  =  2 
gap      0'25 

it  is  evident  that  the  correction  is  negligible,  and  this  is  usually  the 
case. 

Correction  for  Tooth-density. — If  all  the  lines  do  not  pass 
into  the  tops  of  the  teeth,  then  the  mean  tooth  density  as  calculated 
in  the  first  instance  is  also  incorrect.  In  point  of  theory  this  is  the 
case ;  but  in  point  of  fact  it  affects  this  total  ampere-turns  so  little 
as  to  be  negligible  except  in  the  case  of  very  high  tooth  densities. 
For  these  latter,  Hawkins,  Hobart,  and  others  have  given  empirical 
formulse,  but  the  present  author  has  not  found  these  to  be  reliable. 

Ampere-turns  for  High  Tooth-densities. — Often  the  densities 
in  the  teeth  are  so  high  that  they  cannot  be  read  from  ordinary  curves 
like  Fig.  6.  In  such  cases  recourse  may  be  had  to  Fig.  27,  which  is 
the  upper  part  of  a  curve  for  armature  sheets  drawn  to  a  small  scale. 

II.  Leakage  Factor. — The  above  ampere-turn  calculations  again 
are  only  true  on  the  assumption  that  no  magnetic  leakage  exists,  i.e. 
that  the  air  acts  as  a  perfect  magnetic  insulator.  But  if  such  were 
the  case  no  flux  could  cross  the  gap,  and  further,  perpetual  motion 
would  seem  to  be  within  reach. 

Not  only  does  no  magnetic  insulator  exist,  then,  but  none  is  even 
to  be  hoped  for ;  and  from  this  fact  arises  the  necessity  for  making 
various  allowances  for  flux-paths  other  than  those  just  considered. 

Wherever  a  magnetic  potential  difference  exists,  there  a  magnetic 
flux  must  also  be  established ;  and  in  air  this  flux  will  be  directly 
proportional  to  the  ampere-turns  producing  it,  and  to  the  area  of  the 
path,  and  inversely  proportional  to  the  length  of  the  path. 

4 

*  It  is  this  increase  in  ampere-turns  due  to  the  teeth  that  leads  designers  to  adopt 
half-closed  slots  like  Fig.  86,  2,  even  when  such  a  shape  means  putting  the  wires 
in  one  at  a  time.  Verity's  motors  are  sometimes  so  arranged,  and  require,  con- 
sequently, a  very  small  amount  of  field-copper. 


FIELD-MAGNET   CALCULATIONS 


43 


Thus,  if  a  number  of  ampere-turns  act  upon  an  air  circuit,  the 
flux  set  up  is — 

-P,,  mean  area  of  circuit 

ilux  =  ampere-turns  x  A  010 — , rr — ? —       -T. rr 

0'313  x  mean  length  of  magnetic  path 

In  a  circuit  made  up  of  iron  and  air  in  series,  the  iron  part  can 
often  for  a  first  approximation  be  neglected. 

The  mean  area  of  a  leakage-path  and  the  mean  length  of  magnetic 
line  usually  can  only  be  roughly  estimated.  But  the  six  general 
cases  (given  in  Appendix  III.)  will  be  found  convenient  for  reference 
and  calculation. 

Apart  from  calculations  by  such  means  as  are  illustrated  in  these 
cases,  the  most  useful  general  formulae  are  those  evolved  from  the 


150 


140 


130 


120 


1000         2000          3000 

AMPERE-TURNS  PER  INCH. 

FIG.  27. 


4000 


usual  machine  proportions  by  C.  C.  Hawkins.*     The  author  prefers 
to  express  them  here  in  a  modified  form  as  follows  : — 
Total  leakage-flux  per  pole — 

(a)  For  4-pole  machine  =  ampere-turns  per  pole(7'35d  +  D  +  26) 

(b)  For  G-pole  machine  =  ampere  -  turns     per    pole     (8*24d  + 

0,7D  -{-  26) 

(c)  For  8-pole  machine  =  ampere  -  turns     per     pole     (8*37d  + 

0,5-3D  +  26) 
*  Hawkins  and  Wallis,  The  Dynamo,  1903  Ed.,  p.  45. 


44       CONTINUOUS   CURRENT   MACHINE   DESIGN 


where  D  and  d  are  the  armature -diameter  and  diameter  of  pole 
respectively  in  inches ;  or  in  the  case  of  square  poles,  d  =  pole-side, 
as  in  Chapter  I. 

Value  of  Leakage  Factor. — In  Fig.  24  the  chief  leakage  of  flux 
would  occur — 

(a)  From  pole-tip  to  pole-tip. 

(&)  From  pole  to  pole. 

And  since  not  only  (a)  but  most  of  (6)  takes  place  near  the  pole  tip, 
it  is  not  uncommon  for  designers  to  assume  (following  Hopkinson) 
that  practically  the  whole  leakage  takes  place  from  pole -tip  to  pole- 
tip  ;  i.e.  that  the  pole  and  yoke  carry  a  flux  X  times  as  great  as  that 
which  passes  across  the  gap  and  through  the  armature,  where  X  is 
called  the  (Hopkinson)  leakage  factor.  The  following  are  approximate 
values  of  this  leakage  factor  for  ordinary  multipolar  machines,  and 
are  useful  for  preliminary  estimation  purposes  only : — 

TABLE  IV. — APPROXIMATE  LEAKAGE  FACTORS. 
(Machines  of  Medium  Speed.) 


Kilowatts. 

A. 

Kilowatts. 

A. 

5 

1-25  to  1-4 

50 

1.15  to  1-25 

10 

1-25  to  1-35 

100 

11  to  1-2 

25 

1-2  to  1-3 

200  and  over 

1-08  to  115 

Now,  evidently — 

number  of  leakage  lines 
number  of  useful  lines 
reluctance  of  useful  path 
reluctance  of  leakage  path 

ampere-turns  for  a  given  flux  in  the  useful  path 
ampere-turns  to  produce  the  same  flux  through  leakage  path 

Now,  the  chief  reluctances  in  the  useful  path  are  those  of  air-gap 
and  teeth ;  hence 

.  ,  .    ,  reluctance  of  air-gap  and  teeth 

Approximately  X  =  1  H —  £ ,    , TT— 

reluctance  or  leakage  path 

where  for  anjr  path  of  length  /,  and  area  =  A,  permeability  =  /z. 
.p,       _  magneto-motive  force  _     ampere-turns 
reluctance  ~  0*313  reluctance 

Instead  of  reluctance  we  may  write   ;   and  this  is  often 

permeance 


FIELD-MAGNET   CALCULATIONS  45 

more  convenient,  since  the  total  leakage  flux  is  generally  the  sum 
of  leakage  fluxes  along  several  paths  in  parallel,  as  pole-tip  to  pole- 
tip,  pole  to  pole,  etc.  It  is  the  sum  of  these  leakage  fluxes  we 
require,  and  since  permeance  is  directly  proportional  to  flux  while 
reluctance  is  inversely  proportional  thereto,  we  can  add  the  former 
directly  for  various  parallel  paths  acted  on  by  the  same  ampere- turns, 
while  the  latter  cannot  be  so  easily  summed.  This  is,  of  course,  quite 
analogous  to  the  addition  of  "conductances"  for  parallel  electric 
circuits. 

Thus  for  calculation  purposes  the  form 

permeance  of  leakage  paths 
^  =  1  ~f~  permeance  of  air-gap  and  teeth 
is  most  useful ;  where 

Flux  =  magnetomotive  force  x  permeance 

=  ampere- turns  X  permeance  ~  0'313 

Example  of  Approximate  Leakage  Factor  Calculation. — 
We  may  calculate  the  approximate  leakage  factor  for  the  frame 
shown  in  Fig.  24.  The  chief  leakages  will  be  from  pole-shoes  and 
from  pole-cores,  as  already  stated.  The  leakage  from  shoe  to  shoe 
divides  itself  into  two  parts,  viz.  that  between  the  surfaces  parallel 
to  the  shaft,  and  that  between  surfaces  at  right  angles  thereto.  The 
first  falls  under  Case  I.,  p.  226.  Thus — 

Total  ampere-turns  acting  across  the  gap  between  the  shoes  from  one 
pole  to  the  next  =  2  ampere-turns  per  pole 
=  12,412 

leakage  flux  =  12,412  x  *-' ^'xfrSlS*  *'* 
_  12,412  X  21  _llgooo 

Tx~03T3~ '      Ly'ul 

This  takes  place  from  each  side. 

Total  =  119,000  x  2  =  238,000 

For  the  flanks  of  the  shoes  we  may  use  Case  III.,  p.  227. 
The  radius  r  will  be  half  the  polar  arc,  i.e.  =  6  J". 

12,412  00   1-5,        /7T.6-5  + 
Thus  flux  =  -g^g-.  2-3  .-loglo( T- 

=  43,500  X  logw  3-92 

=  26,000 

This  again  takes  place  from  both  flanks  and  in  both  directions. 
The  total  leakage  flux  from  this  cause  is  then 

=  4  x  26,000  =  104,000 

Leakage  between  pole  and  pole  through  the  field-coils. 
As  the  machine  has  circular  poles,  none  of  the  cases  given  will 


46      CONTINUOUS   CURRENT   MACHINE   DESIGN 

apply  directly ;  we  may,  however,  apply  Case  V.,  p.  228,  if  we  allow 
for  the  fact  that  the  poles  are  circular,  by  averaging  the  distance  W. 
Thus  average  value  of  W  (Fig.  28) — 


=  W  +  0-36d  =  20" 

Also  from  Figs.  24  and  136 ;  h  =  T ;  I  =  12 

Leakage  flux  betweenl  =  12,412  x  12 /_  7      2'3  x  20    ^       20    \ 
pole  and  pole          J  =      0'313  x  7    \     2  *      ~~4~~      gl° 20^14 ) 
=  68,000  (-  3-5  +  11-5  logio  3'3) 
=  68,000  (2-8)  =  190,000 

This  takes  place  from  the  pole  to  each  of  its  neighbours. 
Total  leakage  flux  per  pole  from  this  cause  =  380,000. 

Thus  the  total  approximate  leakage  flux 

=  238,000  +  104,000  +  380,000 

=  722,000,  or  say  roughly,  8  x  105  lines 

The  flux  per  pole  we  have  taken  at  10  X  106  lines.  If  we  regard 
this  still  as  the  value  of  the  flux  in  pole  and  yoke,  that  in  the  air- 
gap  and  armature  can  only  be  9*2  x  106  lines,  so  that  all  the  densities 
in  the  latter  portions  need  to  be  recalculated.  If,  on  the  other  hand, 
the  flux  in  armature  and  air-gap  be  taken  as  10  X  106,  that  in  the 
pole  and  yoke  must  be  10'8  X  106,  and  these  densities  must  be 
recalculated.  In  either  case  the  ampere-turns  per  pole  are  changed, 
which  necessitates  recalculation  of  leakage,  so  that  only  by  successive 
approximations  can  the  final  values  be  approached.  It  is  for  this 
reason  Table  IV.  is  given,  that  by  employing  the  value  of  X  taken 
from  this  table  in  the  preliminary  magnetic  calculations  and  check- 
ing back,  much  subsequent  correction  may  be  avoided. 

Assuming  that  10  x  106  is  the  value  of  the  flux  in  air-gap  and 
armature,  then  that  in  the  pole  is — 

1  0*8 

10-8  x  106,  and  X  =  ~  =  1-08 

The  pole  density  corrected  will  be  88,500  X  1'08  =  95,500  ;  and  the 
yoke  density  becomes  47,000. 

These  changes  correspond  to  2080  ampere-turns  for  the  yoke  and 
340  ampere-turns  for  the  pole,  instead  of  1600  and  240  respectively. 
Thus  the  total  ampere-turns  become — 

2080  (yoke)  +  340  (pole)  -f  4140  (gap)  +  156  (teeth) +  70  (armature) 
=  6786  ampere- turns  for  ten  million  lines  per  pole  in  the  arma- 
ture, instead  of  6206  by  the  previous  calculation. 


FIELD-MAGNET   CALCULATIONS 


47 


FIG.  28. 


This  alteration  and  recalculation  could  have  been  saved  by  the 
figure  1*1  from  Table  IV.,  after  which  the  estimate  of  leakage  would 
only  have  been  carried  out  as  a  check. 

It  is  to  be  noted  here  that 
any  factor  necessitating  an  increase 
in  the  ampere-turns  per  pole  in- 
fluences X. 

The  ampere-turns  just  calculated 
are  those  corresponding  to  no-load. 
At  full  load  X  is,  of  course,  greater ; 
but  the  estimation  of  full-load 
ampere-turns  belongs  to  a  later 

chapter ;  here  it  is  of  interest  to  compare  the  calculation  just 
carried  out  with  the  approximation  given  by  the  formula  of 
Hawkins.  „ 

Leakage  flux  =  6$86(7'35  X  12  +  24  +  26) 

=  96  X  104 
leakage  factor  =  1*096 

which  compares  well  with  our  previous  value. 

Leakage  Flux  at  the  Mouth  of  a  Slot  (F.  W.  Carter).— It  is 
sometimes  of  importance  (as  in  the  case  of  interpole  machines)  to 
calculate  the  flux  set  up  at  the  mouth  of  a  slot  which  is  itself  under 
a  pole-shoe.  In  such  a  case  the  flux  across  the  slot  through  the 
ampere-wires  t.  a.  (Fig.  29)  can  be  calculated  under  Case  IV.  (p.  227), 


FIG.  29.— SLOT  LEAKAGE. 


and  the  flux  which  traverses  the  air-gap  directly  from  the  top  of  the 
tooth  as  at  AB  (Fig.  29)  can  be  calculated,  as  also  that  which  passes 
directly  across  the  mouth  of  the  slot  at  CD.  Then  that  which 
springs  from  a  corner  such  as  B  is  obtained  by  multiplying  the 


48      CONTINUOUS   CURRENT   MACHINE   DESIGN 

ampere- wires  of  the  slot  by  the  appropriate  constant  taken  from 
the  curve,  Fig.  30,  and  by  the  net  length  of  the  armature  (or 
interpole)  in  inches. 


1-4 


1-3 


I     1- 


1-1 


1-0 


0-9 


12345 
b/Zg  OE  Zb/g. 

b^width  of  slot. 
p=length  of  air-gap. 

FIG.  30. — SLOT  LEAKAGE — LINES  UNDER  POLE-FACE. 

Magnetization  Curve. — Just  as  the  ampere-turns  corresponding 
to  ten  million  lines  per  pole  have  been  found  to  be  6386  for  the 
machine  in  Fig.  24,  so  for  any  other  flux  per  pole  can  the  correspond- 
ing ampere-turns  be  found.  These  can  then  be  plotted  in  the  form 
of  a  curve  as  shown  in  Fig.  31.  Such  a  curve  is  known  as  a 
"magnetization  characteristic."  It  is  evident  (since  at  constant 
speed  with  no  load  and  a  constant  number  of  armature  conductors 
the  terminal  volts  are  proportional  to  the  flux)  that  for  a  certain 
armature  winding  and  speed  the  ordinates  of  the  curve  may  be 
changed  to  a  volt  scale,  and  when  the  machine  is  built  such  a 
curve  may  easily  be  obtained  on  test  and  compared  with  that 
predicted.  Not  only  for  this  reason,  but  for  its  use  in  calculating 


FIELD-MAGNET   CALCULATIONS 


49 


the   compounding   ampere-turns,   such   a   curve   should   always    be 
drawn  out  for  a  new  machine. 


12 
11 
10 

9 
8 
7 
6 
5 
4 

2 

1 

^ 

-p  250 

x^ 

**^ 

X 

^ 

x 

/ 

/ 

-   150 

/ 

, 

? 

/ 

/ 

/ 

-     50 

J 

01        2       3       4       5       6       7       89       10      11     12 

THOUSANDS  OF  AMPERE-TURNS  PER  POLE. 
FIG.  31. — MAGNETIZATION  CUEVE. 

Interpole  Calculation. — The  calculations  involved  in  connection 
with  interpoles  fall  more  appropriately  under  the  heading  of  com- 
mutation than  of  field-magnets.  They  are  consequently  more  fully 
dealt  with  in  Chap.  IX.,  and  in  the  examples  of  procedure  in  design, 
especially  pp.  194-197  and  p.  209.  The  former  pages  show  the  effect 
on  a  standard  design  which  interpoles  produce. 


CHAPTER    V 

RELATIONSHIP  BETWEEN  ARMATURE  AND 
FIELD  STRENGTH— FIELD  CALCULATION 

FROM  the  calculations  and  corrections  just  considered,  and  from  the 
temperature  rise  factors  dealt  with  in  Chap.  VI.,  the  dimensions  of 
the  field  for  a  given  flux  per  pole  can  be  determined.  The  dimen- 
sions of  the  armature  for  a  given  output  have  also  been  outlined, 
and  we  proceed  to  consider  the  relationship  between  field  and  arma- 
ture. Generally  speaking  there  are  two  ways  in  which  the  dimen- 
sions of  one  of  these  parts  influences  the  other.  It  has  already  been 
shown  that  the  dimensions  of  the  armature  iron  as  forming  part  of 
the  magnetic  circuit  are  dependent  upon  the  flux  per  pole  on  account 
of  the  phenomenon  of  saturation ;  but  the  point  which  has  not  been 
approached  is  the  relationship  between  field  "  strength  "  and  armature 
"  strength  " ;  that  is,  between  the  ampere-turns  of  the  field  per  pole, 
and  the  corresponding  ampere-turns  of  'the  armature.  The  total  of 
the  ampere-conductors  of  the  armature  is  called  (as  already  stated) 
the  "  electric  loading,"  and  the  relationship  therefore  which  we  refer 

to  is  closely  connected  with  the  ratio       "  ,  . — ^ — -^ — -.     Some  short 

electric  loading 

elementary  introduction  is  necessary  to  make  subsequent  reasoning 
clear. 

Armature  Reaction. — So  far  our  calculations  have  proceeded 
without  any  reference  to  the  actual  armature  winding,  and  the 
ampere-turns  have  been  calculated  for  the  field  without  considering 
the  "  back  "  ampere-turns  produced  by  the  armature. 

Now,  for  a  given  output,  flux  per  pole,  and  speed,  the  armature 
ampere-turns  are  fixed  whatever  the  values  of  the  current  and  voltage 
may  be.  Thus  if  we  double  the  voltage  we  halve  the  current ;  but 
the  number  of  conductors  must  be  increased,  with  the  result  that  the 
number  of  armature  ampere-turns  remains  practically  the  same. 

These  armature  ampere-turns  cannot  exist  without  tending  to  set 
up  a  magnetic  field,  for  they  convert  the  armature  into  a  magnetic 
solenoid  whose  axis  is  along  a  line  passing  through  the  conductors 
under  commutation.  This  line  we  call  the  Brush  Axis.  A  glance 


ARMATURE   REACTION 


at  Fig.  32  (which  shows  the  current-circulation  and  armature  field  for 
a  bi-polar  machine)  explains  the  "  armature  reaction."  All  the  wires 
on  the  one  side  of  the  brush  axis  carry  current  in  one  direction, 


R 

armature  AT 
~E 


H 
FIG.  32. — DISTRIBUTION  OP  ARMATURE  FIELD. 

whilst  those  on  the  other  side  carry  current  in  the  opposite  direction, 
resulting  in  the  magnetization  of  the  armature  along  a  line  determined 
by  the  brush  position. 

The  flux  due  to  the  armature  ampere-turns  is  obviously  roughly 
at  right  angles  to  the  field  flux. 

Suppose  provisionally  the  reluctance  of  the  magnetic  circuit  to  be 
the  same  all  round  the  armature.  Let  this  reluctance  be  E. 

Then  total  flux  of  the  field  magnets  = 

Flux  set  up  by  the  armature  = 

The  direction  of  the  resultant  field  due  to  the  two  magnetizing 
forces  may  be  obtained  in 
direction  by  drawing  a 
simple  vector  diagram  with 
AT/  to  represent  the  field 
ampere-turns,  and  ATa  to 
represent  the  armature  am- 
pere-turns (Figs.  33  and  34). 
If  the  reluctance  is  constant, 
this  resultant  gives  the  total 
acting  ampere  -  turns.  In 
practice  ATa  is  not  on  the 
same  scale  as  AT/,  because 
of  the  different  reluctances 
of  the  paths  along  which 
these  ampere-turns  act. 

So  long,  however,  as  the  brushes  remain  in  such  a  position  that 


FIG.  33. — VECTOR  DIAGRAM  OF  ARMATURE 
REACTION. 


AT 


52       CONTINUOUS   CURRENT   MACHINE   DESIGN 

the  armature  magnetic  axis  is  at  right  angles  to  the  field  magnetic 
axis,  little  or  no  weakening  of  the  main  field  results.  But,  if  they  be 
moved  ever  so  little  one  way  or  the  other,  there  is  immediately  a  com- 

ponent of  the  armature  ampere-turns 
ATf  tending  to  weaken  or  strengthen  the 

main  field.  Usually,  commutation 
demands  a  move  in  such  a  direction 
as  to  weaken  the  field,  called  "forward 
lead,"  movement  in  a  reverse  direction 
being  called  "  backward  lead." 

When  the  brushes  are  in  such  a 
FIG.  34.  position   that  the  axis   of   the  con- 

ductors under  commutation  is   also 

the  axis  of  the  resultant  field,  they  are  said  to  be  in  the  "  neutral 
position,"  i.e.  the  line  joining  the  brushes  in  Fig.  33  should  also  be 
at  right  angles  to  the  line  marked  AT.  To  obtain  this  the  brushes 
must  obviously  be  moved  in  the  direction  of  rotation. 

With  the  brushes  in  the  positions  BB1  (Fig.  33),  and  taking  the 
reluctance  as  constant,  then  — 


Resultant  AT  =  \/AT/  + 

The  resultant  is  thus  increased  in  magnitude,  but  altered  in  direction 
as  ATa  increases.  Although  the  resultant  field  is  thus  greater  than 
that  due  to  AT/,  the  E.M.F.  induced  in  the  armature  will  not  be 
larger  because  it  is  only  the  component  of  the  field  at  right  angles  to 
the  brushes  which  can  produce  any  E.M.F.  at  the  brushes  ;  the  other 
component,  being  in  a  line  with  the  brushes,  has  no  effect  on  the 
E.M.F.  between  the  brushes. 

Field  Diagram  with  Brushes  moved  forward  to  the 
Neutral  Position.  —  If  we  move  the  brushes 
forward  until  they  are  in  the  new  "neutral 
position,"  i.e.  until  they  are  at  right  angles 
to  the  resultant  field  just  obtained,  then  the 
direction  of  the  armature  field  will  also  be 
changed,  being  moved  in  the  same  direction 
as  the  brushes.  The  resultant  field  will 
now  be  changed  again,  being  moved  round 
a  little  further. 

The  brushes  in  practice  are  often  moved 
forward  until  they  are  in  the  actual  neutral 
position  (Fig.  35). 

To  show  that  the  Brushes  may  be 
obtained  in  the  Actual  Neutral  Posi- 
tion. —  From  the  above  it  appears  that  moving  the  brushes  round 
will  move  the  resultant  field  round  also,  i.e.  that  the  brushes  can 


FIG.  35.— BRUSHES  IN 
TRUE  NEUTRAL  POSITION. 


ARMATURE   REACTION  53 

never  be  got  into  the  neutral  position.      This,  however,   is   not 
the  case. 

Imagine  the  brushes  moved  forward  to  some  position  in  advance 
of  that  shown  in  Fig.  35.  The  angle  /3  would  then  be  greater  than  a 
right  angle,  so  the  brushes  would  be  in  advance  of  the  neutral  position, 
for  the  two  vectors  ATa  and  AT/  are  supposed  constant  in  magnitude. 

Resultant  Field.  —  With  the  brushes  moved  forward  to  the  neutral 
position  it  is  seen  from  Fig.  35  that  the  resultant  field  AT  is  less  than 
AT/,  besides  being  moved  round  through  an  angle  a. 

In  Fig.  35  if  the  brushes  be  in  the  neutral  position,  i.e.  at  right 
angles  to  the  resultant  field,  then  — 

AT/  =  ATa2  +  AT2 
or  AT2  =  AT/  -  AT2 

Also  let  a  =  the  angle  through  which  the  brushes  are  moved  forward 
to  the  neutral  position,  then  — 


AT, 

Thus  if  we  know  ATa  and  AT/-,  a  may  be  found.   Also  knowing  a  and 
AT/,  AT  may  be  found. 

This  solution  by  vectors,  although  it  gives  a  good  idea  of  what  is 
happening  is  not  of  much  use  in  practice,  because,  as  has  been  said,  the 
reluctances  of  the  two  flux-paths  are  not  the  same,  i.e.  we  cannot 
write  ATa  and  AT/  to  represent  the  fields  unless  they  are  measured 
on  different  scales. 

In  order  to  take  into  account  the  very  different  reluctances  along 
the  field  axis  and  at  right  angles  thereto,  it  is  better  to  consider  the 


ATT 


FIG.  36. — CROSS  AND  BACK  FIG.  37. — RESOLVED  ARMATURE 

AMPERE-TURNS.  REACTION. 

armature  ampere-turns  as  divided  up  in  accordance  with  Figs.  36 
and  37. 

The  total  conductors  do  not  now  act  as  one  complete  "  solenoid," 
half  the  conductors  being  on  each  side,  but  they  are  split  up  into 


54      CONTINUOUS   CURRENT   MACHINE   DESIGN 

two  "  solenoids,"  as  indicated  by  the  dotted  and  chain-dotted  lines. 
The  small  "  solenoid  "  composed  of  the  conductors  at  the  top  and 
bottom  produces  a  field  in  a  line  with  the  main  field  but  opposite  in 
direction  AT'a.     The  other  "  solenoid  "  produces  lines  at  right  angles 
to  the  main  field.     Thus  these  turns  are  known  as  the  back  ampere- 
turns  and  the  cross  ampere-turns  respectively.     From  this  it  is  easily 
seen  that  the  more  the  brushes  are  moved  forward,  the  greater  will 
AT'rt  be,  so  that  the  resulting  field  will  be  weaker. 
Let  Ta  =  total  armature  turns 
and  a  =  angle  through  which  the  brushes  are  moved  (in  degrees). 

Then  total  No.  of  conductors  =  2Ta 
Total  back  turns  = 


_4«Ta 

"  360 

For  a  bipolar  machine  the  current  per  conductor  =  £  total  current 

A.   TP 

.'.  Back   amp.  turns  =  current  per  conductor  x  -^~ 

If  C  =  total  current 

^    ,  C      4aTa      2aTa  x  C 

Back  amp.  turns  =  ^  x  m  =    -3^5- 

m       r^ 

Back  amp.  turns  per  pole  =      *  ' 

Also  cross  ampere-turns  =  total  armature  ampere-turns  —  back 
ampere-turns  (arithmetical  difference). 

Back  AT  in  Multipolar  Machines.  —  With  the  brushes  moved 
forward  through  an  angle  =  a  (Fig.  38),  the  current  in  the  conductors 
has  the  direction  indicated.  The  back  AT  then  consist  of  the 
conductors  lying  under  angle  =  2a,  as  indicated  by  the  dotted 
connecting  lines. 

The  back  ampere-turns  per  pole  are  from  this  diagram  seen  to  be 
in  general  — 

Current  per  conductor  x  ?^  X  total  armature  conductors,  where  a  is 

360 

the  actual  angle  of  brush  lead. 

Use  of  Neutralization.  —  It  is  evident  from  Fig.  32  that  if  a 
solenoid  of  equal  strength  to  the  armature  be  caused  to  act  in  opposi- 
tion thereto  along  the  brush  axis,  nearly  all  the  effects  of  armature 
reaction  may  be  eliminated  and  the  foregoing  calculations  much 
simplified.  This  neutralization  is  accomplished  in  various  ways  which, 
however,  are  considered  under  the  heading  of  commutation  (Chap.  IX., 


ARMATURE   REACTION  55 

Figs.  78  and  79).  The  most  ordinary  method  is  by  means  of 
so-called  interpoles  (p.  121),  and  where  these  are  properly  arranged 
no  addition  to  the  main  field  ampere-turns,  calculated  as  in  Chap.  IV., 
need  be  made.  Where  these  are  not  used  the  total  ampere-turns  on 
the  main  field  coils  must  allow  for  the  armature  reaction.  There  is 


FIG.  38. — ABMATUBE  KEACTION  IN  MULTIPOLAR  MACHINE. 

no  very  satisfactory  means  of  doing  this,  but  those  methods  most 
commonly  in  use  will  be  found  below. 

To  calculate  the  Total  AT  for  the  Field.— There  are  in 
practice  two  methods  of  calculating  the  addition  to  the  ampere-turns 
required  to  compensate  for  the  armature  reaction. 

(1)  Assume  the  brush  lead  to  be  so  great  that  2a  =  angle  between 
pole  tips.  AT&  is  then  calculated  from  this  assumption,  the  cross 
AT  being  neglected.* 

Total  AT  =  AT/  +  AT& 

This  method  allows  ample  AT,  for  the  brushes  are  really  never 
so  far  forward. 

*  It  should  be  obvious,  from  Figs.  36  and  37,  that  the  cross  ampere-turns  cannot 
reduce  the  main  field  strength  directly,  but  only  indirectly,  by  altering  the  saturation 
in  the  teeth  or  pole-shoes.  Thus  where  these  saturations  are  not  great  the  cross 
ampere-turns  can  safely  be  neglected.  For  a  full  detailed  explanation  of  this  point 
see  S.  P.  Thompson's  "  Dynamo-Electric  Machinery,"  vol.  i.  pp.  526,  527, 1904  edition. 


56      CONTINUOUS   CURRENT   MACHINE   DESIGN 

(2)  (a)  The  actual  brush  lead  is  known  from  a  similar  machine. 
The  actual  ATb  may  be  calculated  and  added  to  AT/,  and : — 

(b)  The  cross  AT  are  allowed  for  by  reference  to  experimental 
curves,  such,  for  instance,  as  Fig.  39,  which  purports  to  give  the 
number  of  ampere-turns  (called  "  compensating  "  ampere-turns)  to  be 


0-5 
.  0-4 


,3 

>   0-2 


o-i 


0  2000  4000  6000  8000  10,000  12,000 

Amp. -turns  for  Gap  and  Teeth. 

compensating  amp.-turns 
~     distorting  amp.-turns 
FIG.  39. 

added  to  the  field-coil  to  counterbalance  the  effect  of  the  armature 
cross  ampere-turns  as  increasing  the  saturation  of  the  magnetic 
circuit. 

Examples  of  the  application  of  these  corrections  are  given  on 
pp.  59  and  219. 

Field  Coil  Calculations. — The  calculations  for  the  ampere-turns 
corresponding  to  a  given  flux  per  pole  have  been  explained  and 
illustrated  in  Chap.  IV.,  and  those  required  for  armature  reaction  have 
just  been  estimated.  It  is  necessary  here  to  point  out  that  the  flux 
per  pole  must  be  large  enough  to  provide  for  the  maximum  E.M.F. 
that  the  machine  will  ever  be  called  upon  to  produce.  Thus,  losses 
of  pressure  due  to  load  must  be  allowed  for ;  such  as  those  occasioned 
by  the  resistance  of  the  armature  windings  and  of  the  commutator 
(CEa  and  CEC),  as  also  any  loss  due  to  fall  in  speed  as  load  comes  on, 
etc.  In  a  machine  possessing  only  shunt  coils  all  the  ampere-turns 
required  by  these  various  items  must  be  provided  by  the  shunt 
winding,  and  regulation  for  the  changing  conditions  must  be  obtained 
by  a  variable  resistance  inserted  in  series  with  these  shunt  windings. 
In  a  compound  wound  machine,  on  the  other  hand,  the  shunt  winding 
is  called  upon  to  provide  only  the  ampere-turns  required  to  produce 
that  flux  which  will  give  at  normal  speed  and  no  load  the  proper 
open  circuit  volts. 

The  AT  for  the  series  coil  consist  (1)  of  the  extra  AT  required  to 


ARMATURE   REACTION  57 

increase  the  flux,  so  that  the  total  voltage  generated  by  the  armature 
is  =  the  no-load  voltage  +  the  CE  drop  in  the  armature  and  commu- 
tator, and  in  most  cases  also  the  CE  drop  in  the  series  coils.  Series 
turns  also  take  into  account — 

(2)  AT  necessary  to  counteract  armature  reaction ; 

(3)  AT  required  to  increase  the  flux  so  as  to  make  up  for  drop  of 
volts  due  to  slight  fall  in  speed ; 

(4)  Any  rise  of  voltage  required  to  allow  for  drop  in  feeders  as 
the  load  comes  on. 

Of  these  AT  those  required  for  armature  reaction  are  usually  the 
greatest. 

Having  obtained  the  total  AT  required  for  shunt  and  series  coils 
respectively,  the  watts  to  be  expended  in  each  coil  are  calculated,  as 
suggested  on  pp.  30  and  186. 

Shunt  Coil  Calculations. — Assume  a  constant  PJD.  across  the 
field-coils.  Then 

FIELD  CURRENT  =  C/  =  p- 

where  E/  =  total  resistance  of  all  the  coils. 
If  there  are  p  poles,  then 

C/=  — — 

7         p   X   Tf 

where  ?y  =  resistance  per  coil. 

If  rmt  =  resistance  per  mean  turn,  and  t  =  number  of  turns  per 
coil,  then 

rf  =  rmt  X  t 

•     n  E 

^.e.  (Jf  = 


p  X  rmt  X  t 


and  evidently  the  ampere-turns  per  coil  required  =  tCf. 
Also — 

Ohms  per  yard  of  wire  for  field-coil  =    m.,   v,        .  (2) 

(l*mt) 

where  lmt  =  length  of  mean  turn  in  inches. 

Allowances  for  Insulation  on  the  Wire.— For  small  machines 
not  above  200  volts,  single  cotton-covered  wire  provides  sufficient 
insulation. 

For  single  covering,  O'Ol"  must  be  added  to  the  diameter  of  the 
wire.  This  allows  not  only  for  the  space  occupied  by  the  covering, 
but  also  for  the  "  spring  "  of  the  wire. 


58       CONTINUOUS   CURRENT    MACHINE   DESIGN 

For   large  machines,  and   in   any  case  above  200  volts,  double 
cotton  covering  is  required. 

For  D.C.C.  add  0*018"  to  diameter  of  wire.*     Then 


„                .,              length  of  winding  space 
Turns  per  layer  =  -^  — ? —     &  ,r  .      .     (,- 

•*•  **  /~l  i  o  YYl  firfi-v*    r\T    nr\-*Trk-r*nrl     iTTfr*/^  * 


diameter  of  covered  wire 


(3) 


,          i        p  i  depth  of  coil 

And  number  of  layers  =  -p  -  £—*  -  -,  —  :  — 

diameter  of  covered  wire 


turns  per  coil  =  (3)  x  (4) 

When  worked  out,  the  calculations  should  be  checked  back  by  the 
equation  — 

_  turns  per  coil  X  lmt  X  ohms  per  yard 
Tf=  ~36~ 

and  E/  =  r/  X  p 

(J?\2 

and   v   }     =  watts  lost  in  shunt  field 
rfxp 

which  should  agree  with  the  stipulated  value. 

Arrangement  of  Series  and  Shunt  Coils.  —  By  putting  the 
series  coil  at  the  end  of  the  pole,  high  saturation  of  the  pole  tips 
and  therefore  good  regulation  and  commutation  are  obtained.  How- 
ever, the  series  coil  requires  a  firm  support,  and  when  placed  on  the 
pole-end  a  very  firm  pole  is  required. 

Typical  arrangements  are  shown  in  Figs.  41,  42,  and  43. 

Construction  of  Compound  Coils.  —  The  series  coils  are 
usually  made  up  of  flat  strips,  generally  wound  on  edge.  Eound 
multiple  wire  cable  is  sometimes  used,  but  the  space  factor  then 
comes  out  lower  than  with  strip. 

In  many  series  coils  the  size  of  the  strip  is  so  large  that  it  is 
difficult  to  bend  it  properly,  and  then  the  series  turns  may  be  put  all 
or  partly  in  parallel. 

Whenever  the  strips  can  be  bent  they  should  not  be  put  in  parallel, 
for  if  one  joint  is  worse  than  the  others,  then  there  is  an  unequal 
division  of  the  parallel  currents,  with  consequent  unbalanced  fields. 

Example  of  Preliminary  Calculation  of  a  Compound  Wind- 
ing. —  Let  us  suppose  that  the  machine  in  Fig.  24  is  to  be  provided 
with  a  compound  field  winding  ;  that  the  flux  per  pole  in  the  armature 
at  no  load  is  10  x  106  lines,  and  that  the  no-load  voltage  is  200.  We 
have  already  shown  (Fig.  31)  that  the  ampere-turns  necessary  for 
this  flux  will  be  practically  7000  per  pole,  and  it  is  wise  even  in  a 
compound-wound  machine  to  make  provision  for  emergencies  by 
having  some  resistance  in  the  shunt  field.  Suppose  that  such  a 
resistance  absorbs  10  volts  ;  then  the  pressure  across  the  4  shunt  coils 
is  190  volts.  Now,  if  the  winding  be  arranged  as  in  Fig.  43,  p.  73, 

*  For  more  accurate  details  of  insulation  thickness,  see  p.  139. 


ARMATURE   REACTION  59 

we  may  take  the  depth  of  shunt  and  series  winding  as  2j  inches 
about,  and  their  lengths  as  two-thirds  and  one-third  of  the  total 
winding  length  ;  i.e.  (allowing  for  some  insulation  at  the  ends  of  the 
coils)  as  5  inches  and  2J  inches  respectively.  The  internal  diameter 
of  the  winding  (allowing  for  insulation  between  coil  and  pole)  may 
be  taken  at  12J  inches,  so  that  the  length  of  mean  turn  is  TT  X  (12J 
4-  2J-")  =  46-4  inches. 

From  the  formulae  on  p.  57,  we  have  — 

190 
Eesistance  of  mean  turn  =  j  --  ^nTm  =  ^  ^^  °^m 

,      0-0068  x  36 
ohms  per  yard  =  -      .„. 

=  0-00528 

This  will  be  the  resistance  hot  ;  the  value  cold  may  be  taken  as 
0-00528  -f-  1-16  =  0-0046  ohm. 

The  nearest  wire  to  this  is  No.  14  S.W.G. 

Diameter  bare  =  0'08,  covered  0'098 

5 
turns  per  layer  =  -          =  51 


2'25 
layers  =  =  23 


turns  per  coil  =  1170 

total  turns  =  4680 

yards  =  6000 

resistance,  cold  =  28'7  ohms 
hot  =  33-6  ohms 

190 
C/  =  5^  =5'7  amperes  nearly 

oo'o 

Watts  to  be  dissipated  by  each  shunt  coil  =  270. 

Compound  Winding.  —  We  will  first  suppose  that  the  various 
extras  enumerated  under  the  headings  (1),  (3),  and  (4),  p.  57,  amount  to 
20  volts.  From  Fig.  31  it  is  seen  that  for  220  volts  the  flux  must  be 
11  million  lines  per  pole,  and  that  this  corresponds  to  9000  ampere- 
turns  per  pole.  Thus  the  compound  winding  must  provide  for  9000 
-  7000  =  2000  ampere-turns. 

Back  Ampere  -turns.  —  Estimating  these  by  method  (1),  p.  55, 
we  have,  if  the  output  of  the  machine  is  96  K.W.,  120  amperes  per 
bar,  with  a  4-  circuit  armature  (Chap.  VIII.).  Then 


Back  ampere-turns  per  pole  =  ?84  *^120^x  0-3  =  1728 

Compound  Winding.  —  So  that  total  compounding  ampere-turns 
per  pole  =  3728. 


60      CONTINUOUS   CURRENT   MACHINE   DESIGN 

Now,  the  total  current  of  the  machine  will  be  480  amperes,  and 
if  this  pass  through  the  series  turns,  the  turns  per  pole  will  be  8. 
If  we  allow  1^  volt  drop  in  these  series  turns  (g-  per  cent.), 

1*25 
The  resistance  per  turn  will  be       -  ^  -  johms 


and  the  section  of  the  material  will  be  at  50°  C. 
specific  resistance  X  length  mean  turn 
resistance  per  turn 

76       46-4  x  480  x  8  x  4  „ 

=  10*  X  '          T25-  435  ** 

This  is  heavy  material  to  wind,  but  it  could  be  done  in  a  number 
of  ways.  Thus,  a  copper  ribbon  wound  as  illustrated  in  Fig.  43  could 
be  adopted.  Such  a  ribbon  would  need  to  be  covered  with  braid  or 
tape,  and  ought  to  be  2  inches  wide  by  0'218  inch  thick  ;  or  better 
two  ribbons  in  parallel  each  2  inches  wide  by  0*0109  inch  thick 
could  be  used  ;  either  of  which  arrangements  would  easily  go  into 
the  space  allotted.  These  calculations,  while  illustrating  well  the 
connection  between  dimensions  of  coil,  ampere  -turns,  and  watts 
wasted,  do  not  take  into  account  the  question  of  temperature-rise. 
Further,  nothing  has  been  said  as  to  whether  the  number  of  watts  to 
be  wasted  by  the  shunt  coil  is  right  from  the  standpoint  of  efficiency. 
Consequently,  the  method  given  is  chiefly  of  use  in  calculating  the 
windings  of  standard  machines  in  which  the  relationship  of  these 
quantities  is  known  to  be  about  right.  The  wider  question  is  treated 
in  Chap.  VI.  J  ^  ^^ 

The  Limit  of  Output  imposed  by  Armature  Reaction.  —  It 
has  been  shown  that  when  the  armature  ris  loaded,  the  current 
circulation  is  always  such  as  to  tend  to  form  poles  at  points  inter- 
mediate between  the  field  poles,  and  this  tendency  results  in  the 
distortion  of  the  main  magnetic  field.  Forward  lead  of  the  brushes 
tends  to  accentuate  this,  and  backward  lead  to  diminish  it.  Even 
with  no  lead  some  distortion  exists,  unless  the  armature  ampere- 
turns  are  compensated  by  one  of  the  special  devices  referred  to  on 
p.  121.  Where  no  such  device  exists,  this  interference  largely 
determines  the  ratio  of  field  ampere-turns  per  pole  to  armature 
ampere-turns  per  pole,  and  ultimately  also  the  main  dimensions  of 
the  machine.  For  it  has  been  shown  that,  given  the  densities,  the 
proportions  are  fixed  ;  and  the  field  magnet  is  usually  more  costly  in 
material  than  the  armature.  Thus  increasing  the  ampere-turns  of 
the  armature  results  usually  in  a  cheapened  machine,  and  the  high 
densities  used  in  gap  and  teeth  (which  demand  a  costly  field),  are 
due  to  this  increase  of  armature  strength.  The  question  arises,  then, 
with  the  densities  used,  what  ratio  of  ampere-turns  of  the  armature 


ARMATURE   REACTION  61 

to  ampere-turns  of  the  field  can  be  allowed  ?     The  answei  is  obtained 
only  from  tests. 

Few  machines,  unless  compensated,  show  ratios  exceeding  unity, 
and  general  experience  points  to  the  fact  that — 

(1)  In  shunt-motors  and  compound  dynamos  above  10  K.W.  with 
the  proportions  here  advised,  unity  can  always  be  approached  if  the 
commutator  be  made  with  a  sufficient  number  of  segments.     Often 
it  may  be   exceeded,  1*2   and   1*3   being  obtained.     But  economy 
usually  leads  to  a  ratio  of  about  0*8  (compare  p.  31). 

(2)  In  shunt-dynamos,  attainment  of  a  higher  ratio  is  complicated 
by  the  fact  that  heavy  reaction  goes  with  poor  regulation.     If  this 
be  compensated  by  adjusting  the  shunt-resistance,  the  same  conditions 
hold  as  under  (1).    If  not,  then  a  ratio  of  0*75  to  0*8  will  give  fair 
regulation. 

This  limit  is  largely  a  matter  of  commutation,  and  is  consequently 
dependent  upon  the  choice  of  the  commutation  constants.  Evidently 
also  it  is  dependent  to  some  extent  upon  machine  dimensions.  In 
the  smaller  machines  of  J  to  4  H.P.,  where  high  saturations  cannot 
be  obtained,  the  ratio  comes  out  much  lower,  the  field  ampere-turns 
per  pole  being  often  twice,  and  even  more  than  twice,  as  great  as  the 
armature  ampere-turns  per  pole. 

Senstius,*  who  records  some  experiments  on  this  subject,  con- 
siders that  the  pole-pitch  materially  affects  the  safe  value  of  the 
above  ratio.  He  states  firstly  that  the  maximum  pole-pitch  should 
not  exceed  23  inches,  and  that  for  pole-pitches  varying  from  tfMncEes  ~" 
to  23  inches  the  maximum  ampere-turns  per  pole  for  satisfactory 
designs  vary  from  5000  to  6500  with  average  air-gap  lengths,  the 
lower  figure  corresponding  to  the  smaller  pole  pitch,  and  vice  versa. 
It  will  be  seen  that  this  may  also  be  expressed  in  terms  of  the 
"specific  electric  loading,"  i.e.  in  terms  of  the  ampere -conductors  per 
inch  of  armature  periphery  ;  the  above  values  then  correspond  to 
750  and  600  ampere  conductors  per  inch  respectively  for  pole  pitches 
varying  from  13  inches  to  23  inches.  It  is  interesting  to  compare 
these  with  the  corresponding  values  referred  to  on  pp.  22  and  177. 

Armature  Reaction  in  Neutralized  Machines. — The  value  of 
the  armature  strength  where  special  devices  are  used  to  neutralize  it 
is  determined  solely  by  two  considerations,  viz.  temperature  rise  and 
economy.  The  discussion  of  the  former  will  be  found  chiefly  in 
Chap.  VII.,  but  it  is  of  interest  to  call  special  attention  to  the  limits 
given  by  Senstius  f  (p.  82),  which  would  appear  to  allow  a  maximum 
of  800  ampere-conductors  per  inch  for  a  rise  of  25°  C.,  or  a  maximum 
value  of  1800  ampere-conductors  per  inch  for  a  rise  of  40°  C. 

As  regards  the  latter,  both  theory  and  practice  point  to  a  value 

*  Proc.  Amer.  Inst.  E.E.,  vol.  24,  No.  6,  p.  418.  f  Loc.  cit. 


62      CONTINUOUS   CURRENT   MACHINE   DESIGN 

of  the  armature  strength  considerably  higher  than  that  possible  in 
non-neutralized  machines.  The  increase  of  armature  strength  neces- 
sitates, of  course,  more  copper  for  the  neutralizing  device,  so  that  a 
limit  is  soon  reached  when  further  increase  of  armature  strength 
becomes  too  costly.  This  limit  occurs  (so  far  as  the  author's  experi- 
ence shows)  at  about  1000  ampere-conductors  per  inch.* 

Macfarlane  and  Burge  f  point  out  that  this  maximum  armature 
strength  is  reached  when  the  cost  of  material  in  the  armature  and 
neutralizing  windings  taken  together  is  equal  to  the  cost  of  the 
material  in  the  shunt  winding  and  of  the  effective  iron  and  steel  in  the 
magnetic  circuit.  They  thus  arrive  at  the  conclusion  that  the  ratio 

flux  per  pole  x  No.  of  poles     ,      .,    ,        . 

— T£-     -  should    be    about    300   for    maximum 
armature  ampere-wires 

economy.  In  the  author's  opinion  this  value  is  too  low  for  large 
machines,  where  it  should  be  about  400,  while  300  for  small  machines 
will  be  found  to  give  good  results ;  but  it  is  evident  that  the  choice 
of  this  ratio  (which  undoubtedly  largely  influences  the  cost  of  the 
machine)  is  dependent  partly  on  the  relationship  between  the  cost  of 
the  active  copper  and  iron  and  the  cost  of  corresponding  bed-plates, 
end-plates,  etc.,  which  vary  in  every  works.  Thus  for  safe  designing 
the  value  of  the  best  ratio  must  be  determined  individually  by  every 
manufacturer,  but  the  author  believes  that  when  once  known  it  is 
one  of  the  best  guides,  especially  in  indicating  relative  cost. 

*  Cf.  Page  and  Hiss,  Journal  I.E.E.,  vol.  xxxix.  p.  575. 
t  Journal  I.E.E.,  vol.  xlii. 


CHAPTER   VI 
TEMPERATURE.RISE— FIELD    COILS 

THE  power-losses  which  attend  the  conversion  of  energy  from  one 
form  to  another  manifest  themselves  generally  as  heat.  The  several 
parts  of  the  machine  in  which  these  heat-losses  occur  have  already 
often  been  referred  to,  and  it  is  now  necessary  to  show  in  what  manner 
the  output  of  a  design  is  limited  by  the  consequent  temperature-rise. 
Naturally  the  rise  of  temperature  of  any  part  above  that  of  the 
surrounding  air  will  depend  upon  the  amount  of  loss  in  that  part,  as 
also  upon  the  amount  of  heat  which  the  part  can  liberate  or  dissipate. 
The  extreme  importance  of  this  question  is  now  accentuated  through 
the  use  of  neutralizing  coils  (as  with  interpoles),  which,  by  rendering 
commutation  possible  at  almost  any  load,  remove  what  has  hitherto 
been  one  of  the  chief  limiting  factors  in  dynamo  design.  In  conse- 
quence, where  such  neutralization  is  adopted  the  over-all  dimensions 
are  almost  entirely  dependent  upon  and  determined  by  the  tempera- 
ture-rise of  the  various  parts.  We  shall  therefore  go  into  this  matter 
rather  fully. 

Causes   of  Heat. — The    sources    of    power-loss    occurring    in 
direct-current  machinery  are  as  follows : — 
(a)  In  the  Field  Magnets — 

(i.)  Copper  loss  in  the  windings. 

(ii.)  Eddy-current  loss  in  the  pole-pieces  in  the  case  of 

machines  with  toothed  armatures. 
(5)  In  the  Armature — 

(i.)  Copper  loss  in  the  armature  winding, 
(ii.)  Eddy-current  loss  in   armature   bars.      This  loss   is 
usually    quite    small    and    almost    impossible    to 
estimate. 

(iii.)  Commutator  losses,  comprising  copper  loss  due  to 
contact  resistance  of  brushes,  brush  friction  loss,  loss 
due  to  eddy-currents  in  commutator  bars,  and  loss 
due  to  sparking  (see  pp.  131,  133). 

(iv.)  Iron-losses  in  the  armature  core,  especially  in  the 
teeth  of  toothed  armatures.  These  comprise  hysteresis 


64      CONTINUOUS   CURRENT   MACHINE   DESIGN 

and  eddy-current  energy  losses,  and  methods  of  esti- 
mating them  have  already  been  given  on  pp.  29-30. 
(v.)  Windage  loss  of  armature  and  friction  loss  of  bearings 

(p.  27). 

The  above  power-losses  determine  the  quantity  of  heat  generated 
in  the  field  magnets  and  armature,  and,  with  the  exception  of  (v.), 
vary  with  the  temperature. 

Cooling  Factors. — The  causes  which  contribute  to  the  cooling 
of  the  machine  are  (a)  conduction,  (b)  convection,  and  (c)  radiation. 
The  dissipation  of  heat  by  conduction  is  effected  by  the  iron  core,  the 
copper  conductors,  and  the  insulating  material,  and  evidently  depends 
on  their  ability  to  conduct  heat.  In  the  process  of  convection 
(which  will  also  include  the  conduction  of  the  air)  the  amount  of 
cooling  will  depend  upon  whether  the  machine  is  at  rest  or  rotating, 
open  or  enclosed.  The  most  important  factor  in  the  cooling  of  the 
machine  is  that  due  to  the  radiating  surfaces — that  is,  to  the  superficial 
areas  of  the  conductors  in  direct  contact  with  the  air. 

Laws  connecting  Heating  and  Cooling. — Though  many  ex- 


567 
TIME  IN  HOURS. 

FIG.  40. — HEATING  AND  COOLING  CURVES  OF  A  15  H.P.  D.C.  MOTOR  FOR 
DIFFERENT  LOADS. 

periments  have  been  performed  to  investigate  the  laws  of  radiation, 
yet  our  knowledge  of  the  heat  lost  in  this  way  is  very  scanty,  and 
with  regard  to  convection  we  are  in  almost  complete  ignorance ;  so 
that  we  have  only  approximate  solutions  to  the  various  conditions. 


TEMPERATURE-RISE— FIELD   COILS  65 

Dulong  and  Petit's  exponential  *  law  seems  to  apply  with  better 
accuracy  through  a  wider  range  of  temperature- difference  than  that  of 
Newton,  and  from  the  former  it  follows  that  the  loss  by  radiation  is 
proportional  to — 

(1)  The  size  of  the  radiating  surfaces  of  the  cooling  body. 

(2)  The  excess  temperature  of  the  body  above  the  surrounding  air. 

(3)  The   power   of  emission  of  the   surface,  i.e.   the  nature  of 
the  surface. 

Final  Temperature — When  a  dynamo  or  motor  is  loaded,  the 
generation  of  heat  due  to  the  power  losses  in  any  part  causes  the 
temperature  of  that  part  to  increase,  and  as  this  takes  place  heat  will 
be  emitted  in  the  three  ways  indicated.  The  temperature  continues 
to  rise  until  a  maximum  is  reached,  since  the  rate  of  emission  in- 
creases with  the  temperature  rise.  The  temperature  becomes 
stationary  when  the  rate  at  which  heat  is  generated  is  equal  to  the 
rate  of  its  dissipation. 

Intermittent  Loading. — If  we  had  to  deal  with  the  heating  of 
a  homogeneous  body  which  was  simultaneously  radiating  heat  uni- 
formly over  its  whole  surface,  the  time  taken  for  a  particular 
temperature  rise  would  be  given  by  the  following  equation  : — 


where  0  =  temperature  rise  at  any  time  t ; 

Om  =  maximum  or  stationary  temperature  rise  ; 

T  =  time  constant  depending  on  the  thermal  capacity  of  the 

body. 

The  rise  of  temperature  8  follows  an  exponential  law  as  shown  in 
Fig.  40.  The  value  of  the  time-constant  is  obtained  by  differentiating 
0  with  respect  to  t,  thus — 

di=     m'T'{ 

If  t  =  0,  -=-  =  7^ ;  hence,  since  -*•  is  the  initial  rate  of  heating,  T 
Out        -L  tit 

represents  the  time  which  would  be  taken  for  the  body  to  attain  a 
temperature  rise  9m  if  no  emission  of  heat  took  place. 

If  the  supply  of  heat  were  stopped  and  the  homogeneous  body 
allowed  to  cool,  the  fall  of  temperature  0'  at  a  time  t  would  be 
given  by — 

fit  f\        ~x 

U     =    t/m£ 

*  Dulong  and  Petit's  law  states  that  the  rate  of  cooling — 


where  9t  —  temperature  of  body ; 

6>o  =  temperature  of  surrounding  medium,  and  A  and  a  are  constants. 

F 


66      CONTINUOUS   CURRENT   MACHINE   DESIGN 

Though  the  armature  of  a  dynamo  is  by  no  means  homogeneous, 
the  actual  heating  and  cooling  curves  of  the  direct-current  motor 
given  in  Fig.  40  show  that  the  machine  still  follows  practically  an 
exponential  law  in  the  matter  of  heating  and  cooling.  And  it  is 
possible  from  tests  to  deduce  constants  for  a  given  size  of  machine 
which,  when  used  to  modify  the  formulae  just  derived,  enable  the 
designer  to  predict  with  considerable  accuracy  the  temperature 
rise  on  intermittent  loads — a  most  important  matter  in  crane-rated 
motors. 

Rating  for  Continuous  Working. — It  is  generally  found  that 
the  hottest  parts  of  either  generators  or  motors  of  modern  type 
up  to  250  kilowatts  attain  their  maximum  temperature  within  the 
limits  of  a  six-hour  run  under  continuous  working  with  full  load. 
In  Fig.  40  the  maximum  temperature  of  the  15-h.p.  direct-current 
motor  with  full  load  applied  continuously  is  reached  in  about 
5  hours. 

This  consideration  has  led  the  Engineering  Standards  Committee 
to  issue  the  following  recognized  rating  for  continuous  working  :— 

(A)  The  output  of  generators  and  motors  for  continuous  working 
shall  be  defined  as  the  output  at  which  they  can  work  continuously 
for  six  hours  and  conform  to  the  prescribed  tests,*  and  this  output 
shall  be  defined  as  the  Eated  Load. 

Rating  for  Intermittent  Working. — In  continuous  working 
of  direct-current  machinery  at  any  given  load,  the  heating  and  cooling 
curves  of  the  various  materials  employed  have  little  influence  on  the 
final  temperatures  reached  in  any  part,  but  they  affect  the  time  taken 
to  reach  those  temperatures.  And,  moreover,  since  the  different 
•parts  of  a  machine  are  not  homogeneous,  the  heating  and  cooling  of  a 
particular  part  will  be  affected  by  the  heating  and  cooling  curves  of 
an  adjacent  part  of  different  material.  In  the  case  of  motors  running 
intermittently,  such  as  crane-  and  lift-motors  (which  work  for  short 
periods  and  then  stand  still  so  that  their  field  coils  and  armature  cool 
down  during  the  much  longer  periods  between  each  run),  the  final  rise 
of  temperature  will  evidently  depend  on  the  heating  and  cooling 
curves  of  the  materials  of  the  various  parts.  Let  us  consider  such  a 
motor  to  be  fully  loaded  for,  say,  t  minutes  and  then  to  rest  for  t' 
minutes.  During  the  first,  the  heating  period,  the  machine  will  rise 
in  temperature  to  a  certain  value  along  its  heating  curve ;  it  then 
falls  in  the  next  period  along  the  cooling  curve  for  this  temperature. 
If  these  periods  be  repeated  successively,  the  temperature  of  the 
machine  rises  by  zigzag  amounts,  the  increments  during  the  heating 
periods  becoming  smaller  and  the  decrements  during  the  cooling 
periods  larger.  Hence  the  machine  attains  a  limiting  temperature 

*  These  tests  are  embodied  in  the  temperature  rise  standards  suggested  by  the 
Standards  Committee  on  p.  17  of  the  Keport. 


TEMPERATURE-RISE—  FIELD    COILS  67 

when  the  temperature-increase  during  the  time  of  load  is  equal  to 
the  temperature-fall  during  the  time  of  standstill. 

This  limiting  temperature  will  evidently  be  smaller  than  when 
the  motor  works  continuously,  and  will  depend  on  the  lengths  of  the 
periods  t  and  t'  as  well  as  the  cooling  properties  of  the  materials 
used.  The  time  taken  to  reach  this  temperature  will  also  depend  on 
these  factors. 

It  is  clearly  difficult  to  define  what  shall  constitute  the  output 
for  intermittent  working.  The  Standards  Committee  have,  mean- 
while,* adopted  the  following  definition  of  intermittency  :  — 

(B)  The  output  of  motors  for  intermittent  working  shall  be  the 
output  at  which  they  can  work  for  one  hour  and  conform  to  the  pre- 
scribed tests,  and  this  output  shall  be  defined  as  the  Eated  Inter- 
mittent Load. 

Heating  of  Coils.  —  The  factors  which  determine  the  temperature 
rise  of  a  coil  have  been  shown  above  to  depend  (1)  upon  the  power 
losses  in  the  magnet  coil  ;  (2)  upon  the  size,  shape,  and  nature  of  its 
surface  ;  (3)  upon  the  ventilation  of  the  coil,  i.e.  upon  the  method  of 
support,  whether  closely  fitting  to  the  poles,  or  mounted  on  a  metal 
former  where  there  is  an  air-space  between  the  core  and  the  coil, 
or  provided  with  an  air  space  in  the  middle  of  the  winding  ;  (4)  upon 
the  load  of  the  machine  which  heats  the  armature,  and  thence  by 
conduction  the  magnet-core,  and  by  convection  the  pole-pieces  and 
surrounding  air;  (5)  upon  the  speed  of  the  machine,  an  increased 
circulation  of  air  producing  better  ventilation. 

Investigations  by  Neu  Levine  and  Havill,f  and  recently  at  the 
National  Physical  Laboratory,  t  have  been  made  to  determine  how  the 
mean  temperature  rise  depends  upon  some  of  these  factors,  and  to 
find  the  general  relationship  between  the  maximum  temperature  in 
the  interior  of  any  coil  and  the  mean  temperature  of  the  coil. 

The  mean  temperature  of  a  coil  can  be  measured  accurately  by 
the  increase  of  resistance  of  the  copper  composing  the  winding. 

The  rise  in  temperature  is  given  by  the  following  formula  :  — 

Temperature   rise   in)    _  .^^        .(resistance  (hot)        -,  ) 
degrees  Centigrade  §  I  =  '  (resistance  (cold)  "      f 

*  The  test  is  under  discussion  with  a  view  to  revision. 
t  Electrical  World  and  Engineer,  July  13,  1901,  p.  56. 

J  Report  of  the  Engineering  Standards   Committee  on  Temperature  Experi- 
ments on  Field  Coils  of  Electrical  Machines,  February,  1905. 
§  If  R0  —  the  resistance  of  the  coil  at  0°  C, 

^  =  „  „  T!°  C.  (the  initial  state  of  the  coil,  i.e.  cold), 

RT2  =  „  „  T2°  C.  (the  final  state  of  the  coil,  i.e  hot), 

Then  RTi  =  Ro(i  +  oTl) 
and  RT 


where  a  is  the  temperature  coefficient  of  copper,  viz.  0-00428.     It  represents  the 


68      CONTINUOUS   CURRENT   MACHINE   DESIGN 

.where  t  =  temperature  of  the  room  as  given  by  a  mercury  ther- 
mometer in  degrees  Centigrade  at  which  the  resistance  (cold)  is 
measured. 

The  maximum  temperature  in  Neu  Levine  and  Havill's  experi- 
ments was  obtained  from  the  measurement  of  the  increase  of 
resistance  of  different  sections  of  the  coil,  and  in  the  National 
Laboratory's  results  by  means  of  thermocouples  inserted  during  the 
winding  of  the  coil. 

The  results  of  the  former  on  four  different  coils  show  that  the 
ratio  of  temperature-rise  of  the  hottest  part  to  the  mean  temperature- 
rise  was  1*21  when  the  machine  was  at  rest,  and  1/12  when  running  at 
full  load.  The  National  Laboratory  s  results  show  that  the  difference 
between  the  temperature  of  the  hottest  part  and  the  mean  temperature 
varies  from  about  25°  C.  downwards. 

Temperatures  were  also  taken  by  the  National  Physical  Labora- 
tory by  means  of  a  thermometer  placed  on  the  outside  of  the  coils, 
and  the  results  show  that  the  temperature  rise  varies  with  the 
amount  of  packing  and  local  heating  so  produced.  On  working  out 
the  National  Physical  Laboratory's  results,  the  ratio  of  the  mean 
temperature  rise  to  the  rise  by  thermometer  is  found  to  vary  as 
follows  :  — 

For  taped  coils,  machine  light       .....  17-2  -3 

loaded     .....  1-9-2-5 

„     varnished  coils,  machine  standing  still    .         .         .  1  '4-1*8 

loaded       ....  1-8-2-2 

„  coils  with  taping  removed,  machine  light          .         .  1*2 

loaded       .         .  T4 

The  excess  of  the  maximum  over  the  mean  temperature  varied 
according  to  the  shape  of  the  coil  and  the  temperature  at  which  it 
was  run.  A  large  cooling  effect  on  the  core  side  was  noticeable  in 
the  case  of  some  of  the  coils  wound  on  a  metal  former,  especially 
where  there  was  an  air  space  between  the  core  and  the  coil  ;  and  in 
the  latter  cases  as  low  a  temperature  was  obtained  on  the  core  side 
as  on  the  outside,  when  the  machine  was  running. 

increase  in  resistance  per  ohm  of  the  coil  for  one  degree  Centigrade  rise  in 
temperature. 

aT2)  _  1  +  aT2 


RTl      B0(l  +  aTJ      1 

r,  -  B^       1  +  aT2  -  (1  +  aTQ       a(T2  -  T.) 
RTi  1  +  aT,  "    1  +  aT, 

BT,      \_T 

-  2~  l 


I  -  +  T,  U  —  -^  —  1  )  =  rise  in  temperature. 


TEMPERATURE-RISE— FIELD   COILS  69 

This  is  further  borne  out  by  E.  Brown's  *  observations  on  a  bipolar 
Siemens  dynamo.  He  notes  the  following  points : — 

(1)  The  bobbin  .flanges  have  an  influence  on  the  cooling,  and 
should  be  made  of  as  good  conductors  of  heat  as  is  possible  consistently 
with  their  insulating  properties. 

(2)  The  magnet-core  is  efficacious  in  promoting  cooling,  hence 
any  layers  between  the  coil  and  core  should  be  good  conductors  of 
heat. 

(3)  The  highest  temperatures  are  in  the  middle  of  the  coil,  and 
it  should  be  made  less  deep  there. 

In  the  National  Laboratory's  experiments,  two  similar  coils, 
having  the  same  number  of  watts  expended  in  each,  but  wound  with 
different  gauges  of  d.c.c.  wire,  showed  an  appreciably  lower  tempera- 
ture rise  for  the  coil  with  the  smaller  amount  of  cotton,  the  coils 
being  suspended  in  air. 

Berrited  wire  produces  a  considerable  reduction  in  the  temperature 
rise,  as  does  also  little  or  no  covering  on  the  coil.  The  following  tem- 
peratures were  observed  on  two  similar  coils,  one  wound  ordinarily 
and  covered  with  a  layer  of  empire  cloth  and  a  layer  of  varnished 
tape,  and  the  other  wound  with  berrited  wire  and  no  covering  : — 

With  covering.        Without  covering 
and  berrited  wire. 

Maximum  temperature  above  air       .       80°  C.       .       54*9°  C. 
Mean  „  „  .    63*6°  C.       .       46-9°  C. 

Limiting  Temperatures  for  Coverings. — Experiments  seem 
to  show  that  the  limiting  temperature  for  cotton- covered  wire 
is  about  125°  C.,  at  which  cotton  begins  to  darken;  though  up 
to  180°  C.,  when  it  is  nearly  black,  it  is  still,  from  the  electrical 
point  of  view,  a  good  insulator  as  compared  with  cotton  at  atmo- 
spheric temperature. 

Temperature  -  rise  Standards. — The  Engineering  Standards 
Committee  suggest  the  following  temperature-rises  for  machines  in 
which  cotton,  paper  and  its  preparations,  linen,  vulcanite,  and  similar 
insulating  materials  are  used : — 

Stationary  coils  (by  resistance)         .  .         .     60°  C.  (108°  F.) 
Moving  coils  (by  resistance)     .         .  .  60°  C.  (108°  F.) 
Moving    coils   (by   thermometer  or  thermo- 
couple placed  in  contact  with  coil  or  core, 
whichever  be  the  hotter)      .  .  .                50°  C.  (90°  F.) 

These  temperature  rises  are  based  on  the  assumption  that  the  air 
temperature  is  not  greater  than  25°  C.  (77°  F.).  If  the  air  temper- 
ature is  greater,  then  each  of  the  temperature  rises  specified  must  be 

*  Journal  of  Inst.  E.E.,  xxx.  1159,  1901. 


70       CONTINUOUS   CURRENT   MACHINE   DESIGN 

decreased  by  one  degree  for  each  degree  difference  between  the  room 
temperature  and  25°  C. 

In  all  cases  the  temperature-rise  observed  during  actual  service 
of  the  machine  must  be  such  that  the  mean  temperature  of  the 
machine  shall  not  exceed  85°  C.  (185°  F.). 

Where  the  insulation  consists  of  special  materials  to  resist  high 
temperatures,  and  also  where  cotton,  paper,  linen,  etc.,  are  used  as 
vehicles  for  varnishes  and  enamels,  the  permissible  temperature  rise 
depends  on  the  properties  of  the  insulating  materials  and  the  method 
of  construction. 

Heating. — For  a  given  coil  the  temperature-rise  is  found  to  be 
practically  proportional  to  the  watts  dissipated  in  it.*  If  we  desire 
to  employ  an  empirical  rule  connecting  the  coil-surface  with  the 
assigned  limiting  temperature  rise,  it  will  be  convenient  to  employ  a 
coefficient  C/t,  called  the  heating  coefficient,  or  specific  temperature 
increase. 

Then  if  PTO  =  watts  wasted  in  the  magnet  coil, 
A™  =  cooling  surface  of  the  coil, 
T    =  mean  temperature  rise  assigned, 

T  =  C,  x  |? 

•A-m, 
p 

The  fraction  -r7""  may  be  termed  the  specific  power-loss,  i.e.  the 
ATO 

watts  dissipated  per  unit  surface.  If  the  specific  power-loss  is  unity, 
then  CA  =  TI  ;  that  is,  the  heating  coefficient  is  the  temperature  in- 
crease when  one  square  inch  dissipates  one  watt.  The  coefficient 
Cfc  will  depend  on  the  factor  we  have  already  discussed  when  con- 
sidering the  radiation  of  the  coil,  and  it  is  interesting  to  compare  the 
values  already  given  by  various  authors. 

At  the  very  outset  one  is  struck  with  the  want  of  decision  on 
points  which  would  seem  to  be  of  the  greatest  importance.  Thus, 
how  the  temperature  is  to  be  measured,  how  the  coil  is  shaped  and 
covered,  or  how  the  cooling  surface  for  the  formula  is  to  be  estimated, 
are  details  little  discussed  and  often  left  entirely  to  the  reader's 
discretion.  We  may,  however,  roughly  tabulate  the  directions  and 
constants  as  follows : — 

*  See  p.  8,  N.P.L.  Report,  No.  19. 


TEMPERATURE-RISE— FIELD   COILS 
TABLE  V. 


30DC. 
Thermometer. 

50°  C. 

Resistance. 

Surface. 

Esson  *  .     . 
Kapp     .  4 
Wiener  t     . 

0-55 
0-75 

0-68 

Exposed. 
Exposed  to  air. 
Exposed  surface  and  flanges 
if  air  has  access  to  them. 

Thompson  J 

— 

0-67 

Exposed  surface,  not  includ- 
ing    flanges    or    internal 
surfaces. 

Oerlikon  § 
Goldschmidt  || 

— 

0-45 
0-21 

Ditto. 
Total   surface,   interior   and 

exterior. 

Hobart  If    . 

0-67 



Cylindrical  surface. 

Neu    Levine 
andHavill** 

(average) 

0-45 

Cylindrical     surface,     with 
special  allowances  for  coils 

near  iron. 

Arnold  ft    . 

j      — 

0-43  to  0-65 

/           Long.                Short  (thick). 

k     ^                    N|     f          •?                       Y 

1           1      I!           | 

Areas  chosen. 

\ 

It  will  be  seen  that  on  the  whole  Arnold's  are  the  most  explicit 
directions,  but  even  these  leave  a  large  margin  for  discretion. 

Now,  this  margin  may  be  much  reduced  by  reference  to  recent 
experiments,  and  the  author,  in  collaboration  with  Mr.  J.  Lustgarten, 
has  made  a  careful  comparison  of  such  as  he  has  been  able  to  find,  the 
most  important  contribution  being  that  of  the  National  Physical 
Laboratory. 

*  S.  P.  Thompson,  "  Dynamo-Electric  Machinery,"  vol.  1,  p.  182.     1904. 

t  Wiener,  "  Dynamo-Electric  Machines,"  p.  369.     1902. 

t  S.  P.  Thompson,  "Dynamo-Electric  Machinery,"  vol.  1,  p.  184.    1904. 

§  Ibid.,  p.  183. 

II  Journal  Inst.  E.E.,  vol.  34,  p.  665.     1905. 

f  Hobart,  "  Continuous-current  Dynamo  Design,"  p.  90.     1906. 

**  Loc.  tit.,  p.  67. 

ft  "  Die  Gleichstrommaschine,"  vol.  1,  p.  520. 


72       CONTINUOUS   CURRENT   MACHINE   DESIGN 

This  comparison  leads  to  the  following  conclusions  : — 

1.  That  the  surface  for  cooling  to  be  taken  into  account  should 

include  the  whole  surface,  i.e.  the  external  cylinder,  the 
internal  cylinder,  and  both  ends. 

2.  That  these   surfaces,  however,  are  not  all  equally  valuable  as 

radiators. 

3.  That  the  surfaces  of  the  coil  in  direct  contact  with  free  air  and 

those  next  to  metal  flanges  in  direct  contact  with  free  air  are 
the  best  for  dissipating  heat,  and  are  about  equally  valuable 
from  this  point  of  view. 

4.  That  coil  surfaces  next  to  the  iron  of  the  pole  or  yoke,  or  next  to 

a  former  fitting  the  pole,  or  so  close  to  the  yoke  that  no  air- 
current  is  available  are  about  half  as  valuable  as  surfaces 
such  as  those  under  (3). 

5.  That  surfaces  spaced  apart  from  the  pole  or  yoke,  so  as  to  allow 

a  free  air-current  between  them,  have  a  value  intermediate 
between  3  and  4. 

6.  That  different  values  of  Ch  must  be  chosen  according  to  the  depth 

of  the  coil  winding  and  the  taping  and  insulation  of  the  coils. 


10* 


FIG.  41. — FIELD-COIL  ON  SHEET-METAL  FORMER. 

These  considerations  lead  the  author  to  recommend  the  following 
constants  for  the  estimation  of  temperature  rise  of  field  coils. 
In  the  formula — 

TO  _  p    v  "m 
*  X  A~ 

•^m 

AOT  is  estimated  for  the  whole  coil,  and  is  the  sum  of — 
All  surfaces  included  under  (3)  ; 
Half  the  surfaces  included  under  (4)  ; 
From  07  to  O8  of  the  surfaces  under  (5). 
The  values  of  Ch  then  are— 

A.  (Figs.  41  and  42)  For  coils  on  metal  formers  with  no  external 
taping,  and  a  depth  not  exceeding  3" — 
Ch  =  130  to  150 


TEMPERATURE-RISE— FIELD   COILS 


73 


—  130  is  to  be  used  only  where  the  coil  is  well  below  3"  in 
depth  ;  150  is  a  good  safe  value. 


< 


I 

FIG.  42.— -"FIELD-COIL  ON  CAST-IBON  FORMER. 

B.  (Fig.  43)  For  coils  with  two  or  three  layers  of  tape  around  them — 

Ch  =  200 

If  impregnated   and  taped,  a  somewhat  lower  value   may  be 
taken,  as — 

ft  =  180 

C.  For  coil&Jwrapped  in  canvas,  fullerboard,  etc.,  up  to  a  thickness 

of  J-"  all  over — 

Ch  =  220 

Where  an  exceptional  depth  of  coil  is  used,  as  5",  C^  must  be 


eft 

i 
I 
t 
Y 


13" 


FIG.  43. — TAPED-COMPOUND  COIL. 


FIG.  44. 


increased  slightly,  usually  10  per  cent,  to  15  per  cent,  for  each  inch 
of  depth  above  3". 

T  is  from  15°  to  25°  C.  higher  than  the  temperature  measured  by 
thermometer. 

Deductions  from  the  Results. — The  results  just  summarized 


74       CONTINUOUS   CURRENT   MACHINE   DESIGN 

are  remarkable  in  many  ways,  but  especially  in  pointing  the  advan- 
tage to  be  gained  by  proper  ventilation  of  the  field  coils.  It  is  very 
clear  that  leaving  room  for  air  circulation  about  a  coil  will  increase 
by  no  inconsiderable  amount  the  watts  which  that  coil  can  dissipate 
(for  a  given  temperature-rise).  This  advantage  will  depend  upon 
many  factors,  but  chiefly  upon  the  relationship  between  the  depth  of 
the  winding  (dc  in  Fig.  44)  and  the  internal  diameter  of  the  coil  (2r2 
in  Fig.  44). 

Now — 

2r2  =  diameter  pole  +  clearance  for  air  circulation 

=  diameter  of  pole  +  2(|"),  usually, 

so  that  the  advantage  to  be  gained  will  depend  very  largely  on  the 
relationship  between  the  diameter  of  pole  and  depth  of  coil. 

Depth  of  Coil. — The  depth  of  coil  which  is  found  to  be  of  use  in 
practice  is  curiously  constant.     In  modern  machines,  it  only  varies 


FIG.  45. — FIELD-COIL  DIVIDED  FOR  VENTILATION. 

from  27  in  machines  of  4  H.P.  up  to  4"  (or  very  rarely  5")  in  machines 
of  the  largest  size ;  and  since  the  diameter  of  the  pole  is  by  no  means  so 
constant,  there  will  be  a  size  of  machine  below  which  it  does  not  pay 
to  insert  these  ventilating  spaces.  Naturally  this  limit  depends f 
largely  upon  many  variables,  not  the  least  of  which  is  the  price  of 
copper,  so  that  it  is  difficult  to  fix  even  approximately ;  but  the  author 
would  place  it  at  about  30  kilowatts. 

In  machines  of  80  kilowatts  or  more,  it  becomes  economical  to 
break  up  the  field  coil  into  a  number  of  sections  as  shown  in  Fig.  45. 

These  may  be  from  1"  to  2"  in  length,  with  air  spaces  of  f"  to 
1"  all  round.  Fig.  93  shows  a  method  devised  by  the  author  for 
fixing  insulating  and  ventilating  compound-wound  field  coils. 

General  Formulae. — From  the  summary  on  pp.  72,  73,  for  any 
given  shape  of  coil  general  and  particular  formulas  may  be  easily 
derived. 


TEMPERATURE-RISE—  FIELD   COILS  75 

CASE  I.  The  upper  annular  and  inner  cylindrical  surfaces  of  the 
coil  in  Fig.  44  are  supposed  spaced  apart  from  the  yoke  and  pole 
respectively,  and  fall  under  paragraph  5  on  p.  72.  Then  if  the  pole 
be  circular  in  section,  and  k  is  the  fraction  of  the  surfaces  not  fully 
exposed  to  air,  considered  as  effective  under  these  paragraphs  — 

AM  =  ird^l  +  k)  +  2irr2(lc  +  dc)(l  +  k)  +  2irdclc 
with  k  =  0*75  this  becomes  — 

Am  =  5'5^2  +  Ilr2(lc  +  dc)  +  6'28^c 

If  the  pole  be  square  in  section,  then  in  Fig.  44  r2  =  (J  width  of  one 
side  of  pole  +  clearance),  and 

Am  =  8/.K  +  r2(l  +  K)}  +  Uc(dc  +  2r2)(l  +  k) 
Or  if  A;  =  075 

Am  =  Id?  +  Slcdc  +  14ra(Jfl  +  dc) 

CASE  II.  The  field  coil  is  supposed  to  fit  pole  and  yoke  closely. 
Here  k  =  0*5,  so  that  for  circular  poles  the  equation  is  — 

Am  =  4-7rfc2  +  9-4r2(4  +  de)  +  6'28UC 
For  square  poles  it  is  — 

Am  =  6^c2  +  8WC  +  12r2(^c  +  dc) 

CASE  III.  Coil  divided  into  sections  *  (Fig.  43).  The  lowest  section 
may  be  taken  under  Case  I. 

For  each  of  the  other  sections  with  circular  pole  — 

Am  =  27r(r2  +  de)le  +  k{2irrJ0  +  27r(2r2  +  dc)dc} 
If  k  =  0-75— 

Am  =  ±7dc*  +  9-4r^0  +  llr,lc  +  6'28dclc 
With  square  pole  — 

AM  =  8/c(r2  +  de)  +  k{Sr2lc  +  8(2r2  +  dc)dc} 
=  0-75- 

Slcdc 


Often  the  value  of  dc  can  be  approximately  fixed,  and  when  this 
is  so  the  foregoing  equations  give  the  values  for  lc,  because  CA,  T, 
and  Pm  are  all  known  from  the  circumstances  of  the  case. 

Example.  —  We  are  now  in  a  position  to  illustrate  these  calcula- 
tions by  completing  the  field-coil  which  was  calculated  on  p.  59. 
We  shall  start  this  time  from  the  supposition  (generally  true  for  new 
machines)  that  the  watts  to  be  dissipated  are  known  roughly  from  the 
desired  efficiency,  and  that  the  temperature  rise  is  fixed. 

We  shall  suppose  that  the  ampere-turns  to  be  provided  per  pole 
are  those  previously  calculated,  viz.  about  7000  for  the  shunt,  and 

*  In  which  case  Zc  refers  of  course  to  the  length  of  one  section. 


76       CONTINUOUS   CURRENT   MACHINE   DESIGN 

3800  for  compounding.  Further,  that  the  watts  allowable  for  each 
shunt  coil  are  about  275,  which  with  a  voltage  of  190  across  the  4 
coils  corresponds  to  C/  =  5*7  amperes. 

The  watts  to  be  expended  in  each  series  coil  are  150  ;  and  the 
series  current  is  480  amperes,  corresponding  to  8  turns  per  pole.  The 
series  coil  is  to  be  placed  nearest  the  pole-tip,  and  the  shunt  coil  is 
to  be  divided  (if  necessary)  into  two  or  more  sections  to  secure  the 
requisite  cooling  surface.  The  coils  are  all  to  be  taped  and  impreg- 
nated ;  T  =  60°,  Cfc  =  180.  It  will  be  of  interest  first  to  examine  such 
an  arrangement  as  that  already  calculated  on  p.  59,  to  see  if  it  can 
fulfil  the  stipulated  conditions. 

Considering  first  the  shunt  coil  alone,  we  have — 

ATO  =  Ch~  =  180  .  2g£  =  825 
Applying  Case  II.,  taking  r2  =  6" 

So  that— 

ld  __  825  -  4-7^c2  -  66-4(1,  +  d.)  (1) 

Now,  this  equation  connects  lc  and  dc ;  and  a  second  equation 
connecting  the  same  two  quantities  may  be  obtained,  as  is  shown  in 
Appendix  IV.,  p.  230. 

If  we  remember  that  the  specific  resistance  must  be  that  of  the 

QO 

material  when  hot,  say  r^  ohms,  and  that  the  length  of  mean  turn 

will  be  7r(2r2  4-  de),  we  obtain  from  the  second  equation — 

_  4    82  X  (ampere- turns  per  coil)2  X  7r(2r2  +  dc)  x  m2 
c  c  ~~  TT  *  ~  108  X  watts  per  coil 

diameter  of  wire  covered 
where  m  is  the  ratio    diameter  of  wire  bare  ' 

The  diameter  of  the  wire  is  known  to  be  in  the  neighbourhood  of 
No.  14  d.c.c.  (cf.  p.  59),  for  which  from  any  wire  tables  m2  is  found 
to  be  about  1*4. 
Thus— 

82  x  7000  X  7000  x  «{12  +  de)  x  1-4  ,  4-     /9^ 

I  Ci       = 5 ~~      *  .  r         (*-l ) 

108  x  215  ^  77 

If  we  take  the  value  of  dc  for  which  the   coil   was   originally 

arranged,  viz.  2J",  we  find  from  these  equations  lc  =  10",  which  with 

a  pole  of  8"  is  manifestly  impossible. 

If,  on  the  other  hand,  we  take  the  maximum  permissible  depth 

consistent  with  reasonable  temperature  in  the  coil  centre,  viz.  4", 

we  find,  when  the  series  winding  is  considered,  lc  =  more  than  9", 

which  is  still  impossible. 


TEMPERATURE-RISE— FIELD   COILS  77 

Thus  an  un ventilated  winding  such  as  that  proposed  in  Chapter  V. 
is  impossible  from  the  point  of  view  of  temperature  rise. 

Calculation  of  Ventilated  Coil.  Shunt  Winding. — Suppose 
now  that  we  space  the  shunt-coil  1"  from  the  pole  all  round,  and  divide 
it  into  two  sections.  Then  each  section  may  be  taken  under  Case  III., 
and  below  the  two  shunt-coils,  if  there  is  room,  we  can  put  the  series 
turns. 

Evidently  each  section  of  the  shunt-coil  must  dissipate  ^15 
=  14&f  watts ;  and  the  length  of  mean  turn  will  be  7r(14  -f  dc). 

\^>f].5                                      275 
Also  Am  =  180  X  g~ s  =  412  sq.  ins. 

OU  X  ^ 

*  Equation  (1)  is,  from  Case  III. — 

412  =  4W  4-  66dc  +  77/c  +  Q"28dclc    ...     (1) 

*  Equation  (2)  is — 

82      (70QQ)2      7r(14  +  d.)  X  1-4 
•  ~  io8  x     4 


=  4-4  + 
whence  we  obtain : — 

d0  =  3",  4  =  1-8" 

If  we  allow  a  space  of  £"  between  yoke  and  coil  for  air,  and  |" 
between  one  section  of  the  coil  and  the  next,  we  shall  have — 
Length  of  shunt-coil  =  0'75  +  I'S  +  075"  +  1-8" 

=  5-1" 

Series-winding. — Taking  now  the  series-coil  under  Case  L, 
and  of  the  same  depth  as  the  shunt,  we  have — 

450  =  5-5  x  (3)2  +  11  X  7(4  +  3)  +  6'28  x  34 
Am  =  180 . 1650°-  =  450 

whence  4  =  2"  practically ;   and  this  allows  of  ventilating  spaces 
between  shunt-  and  series-coils. 

Thus  with  an  unventilated  coil  the  shunt-winding  alone  will  hardly 
go  in,  whilst  with  ventilation  there  is  room  for  both  shunt-  and 
series-coils. 

Size  of  Wire. — The  turns  per  section  of  the  shunt-coil  will  be — 

~= 2  =  623  about 

and  since  m2  x  (diameter  of  wire)2  =  c 


diameter  of  wire  = 


623  X  1-4 
=  0-0787 
which  is  practically  14  S.W.G-. 

*  These  pairs  of  equations  lead  to  one  of  cubic  form,  difficult  to  solve.     Usually 
the  best  way  of  dealing  with  them  is  by  means  of  squared  paper. 


78      CONTINUOUS   CURRENT   MACHINE   DESIGN 

The  current-density  is  about  900  amperes  per  square  inch,  and 
the  size  of  the  series-winding  can  be  calculated  as  shown  on  p.  60. 

Notes  on  the  above  Calculations. — The  method  of  field-coil 
calculation  just  outlined  is,  so  far  as  the  author  is  aware,  the  first  to 
attempt  any  rigid  connection  between  the  four  quantities,  ampere- 
turns,  watts  lost,  coil-dimensions,  and  temperature-rise.  If  used  with 
discretion  it  will  be  found  to  be  reliable,  but  it  is  naturally  open  to 
various  errors,  and  the  reader  should  be  alive  to  these.  In  the  first 
place,  the  equation  from  which  lc  is  derived  is  of  the  form— 

A  -  B 

7TT 

which  is  always  unsatisfactory,  since  when  A  and  B  are  large  and 
comparable,  a  small  percentage  change  in  either  will  alter  the  value 
of  lc  so  much. 

Next  the  value  chosen  for  CA  naturally  affects  the  results  con- 
siderably, and  some  experience  is  necessary  to  judge  the  conditions 
likely  to  affect  the  choice.  These  include  effect  of  armature -windage, 
shape  of  field,  amount  of  protection,  and  clearances  allowed  in  the 
case  of  ventilated  coils. 

Cost  of  Ventilated  Coils. — It  is,  of  course,  obvious  that  the 
amount  of  copper  involved  in  the  ventilated  coils  with  an  8 -inch  pole 
is  greater  than  that  required  for  a  close-fitting  coil  with  a  longer  pole. 
The  latter,  however,  involves  greater  weight  of  material  in  poles  and 
yoke,  so  that  only  by  a  careful  comparison  of  the  cost  of  material  in 
the  two  cases  can  the  most  economical  design  be  arrived  at. 


CHAPTER   VII 

TEMPERATURE-RISE— ARMATURES  AND 
COMMUTATORS 

Heating  of  Armatures. — The  losses  which  occur  in  the  armature 
causing  and  resulting  in  "  temperature-rise  "  have  been  enumerated 
on  p.  63.  It  may  here  be  pointed  out  that  great  differences  are 
often  found  between  the  calculated  and  the  actual  values  of  the  iron 
losses.  This  lack  of  agreement  depends  to  a  great  extent  on  the 
amount  of  burring  over  of  the  discs,  and  will  be  more  marked  at  the 
higher  inductions  ;  by  careful  milling  or  filing  it  can  be  considerably 
reduced.  (See  footnote,  p.  204.) 

The  amount  of  heat  liberated  from  the  armature  will  depend 
chiefly  on  the  heat-radiating  surface.  In  estimating  this  surface  we 
shall  have  to  consider  the  influence  of  the  core  and  the  spider.  The  core, 
though  much  of  it  is  covered  with  insulation,  is  a  good  conductor  of 
heat ;  and  the  inner  surfaces,  including  the  spider,  offer  great  facilities 
for  dissipation  of  heat  where  a  good  circulation  of  air  is  obtained.  This, 
for  example,  is  the  case  where  the  armature  is  provided  with  three  or 
four  ventilating  ducts,  as  in  Figs.  3  and  110.  The  end-connections 
in  former-wound  armatures  are  arranged  to  allow  of  a  good  circula- 
tion of  air  to  the  spider,  and  also  have  an  excellent  fanning  action. 

A.  H.  and  C.  E.  Zimmerman  *  found  that  as  the  peripheral 
velocity  of  the  armature  is  increased,  the  amount  of  heat  liberated 
per  degree  rise  in  temperature  is  also  increased ;  but  that  the  rate 
of  increase  becomes  less  with  the  higher  speeds.  The  influence 
of  the  peripheral  velocity  on  the  cooling  will  depend  chiefly  on 
the  construction  of  the  armature-core,  the  arrangement  of  the 
winding,  and  the  disposition  of  the  field-poles.  The  latter  tend  to 
prevent  the  radiation  of  heat ;  and  as  the  percentage  polar  embrace 
increases,  the  amount  of  heat  radiated  per  degree  rise  in  temperature 
becomes  less. 

The  rise  in  temperature  of  the  armature  will  also  be  influenced 
by  the  ventilation  of  the  room  in  which  the  machine  is  placed,  so 

*  A.  H.  and  C.  E.  Zimmerman,  Trans.  Am.  Inst.  Elec.  Engs.,  vol.  x.  p    336 
(1893). 


8o      CONTINUOUS   CURRENT   MACHINE   DESIGN 

that  a  machine  standing  in  a  draughty  place  usually  has  a  low  tem- 
perature, since  cooling  by  convection  is  more  effective  than  by 
radiation.  It  is  for  this  reason  that  fans  have  recently  been  intro- 
duced (Fig.  124)  in  motors  to  cause  a  definite  current  of  air  through 
the  armature. 

Measurement  of  Armature  Temperature. — The  end-connec- 
tions (both  front  and  back)  cool  usually  better  than  the  part  of  the 
winding  embedded  in  the  slots,*  and  since  the  length  occupied  by 
these  connections  is  sometimes  as  much  as  three  times  that  of  the 
armature  core,  it  would  be  scarcely  fair  to  estimate  the  temperature 
of  the  latter  by  the  "  increase  of  resistance  "  method.  As  the  induc- 
tion is  greatest  in  the  teeth  of  the  armature,  the  iron  losses  also  will 
be  greater  there,  and  the  maximum  temperature  will  be  registered 
better  by  a  thermometer.  In  testing  armatures  for  temperature-rise 
after  the  run,  thermometers  are  required  for  the  winding,  for  the 
armature  iron,  and  for  the  commutator.  They  are  held  in  place  by 
means  of  small  pieces  of  cotton- waste  wedging  their  backs  (which  are 
sometimes  covered  with  tin-foil)  against  the  surface.  These  pieces 
of  waste,  by  reason  of  their  low  conductivity,  prevent  the  radiation 
of  heat  from  the  thermometer  when  its  temperature  is  above  that  of 
the  surrounding  air.  The  thermometers  are  left  in  place  until  their 
readings  begin  to  decrease,  usually  from  10  to  15  minutes.  The 
highest  temperature  is  generally  found  between  two  ventilation  ducts 
in  the  middle  of  the  armature.  The  temperature  thus  actually 
measured  is  higher  than  that  which  ever  occurs  when  the  armature 
is  running,  because  directly  rotation  ceases  the  dissipation  of  heat  is 
very  much  reduced. 

Methods  of  estimating  Temperature  Rise. — As  in  the  case 
of  field-coils,  so  again  here  authors  are  often  quite  indefinite  as  to 
the  surface  to  be  used  for  estimation.  It  is,  however,  universally 
admitted  that  an  expression  of  the  form — 

T  -  -JL- x  P 
"  1  +  Iv  x  A 

gives  the  best  approximations.  In  this  formula  a  and  b  are  constants, 
v  is  the  linear  circumferential  velocity  of  the  armature  in  feet  per 
minute,  P  is  the  number  of  watts  to  be  dissipated,  and  A  the  area  of  the 
surface  of  the  armature  in  square  inches.  T  is  in  degrees  Centigrade. 

There  is  some  difficulty  in  properly  estimating  the  quantity  P,  but 
the  real  trouble  is  in  deciding  upon  what  basis  A  shall  be  computed. 

The  Value  of  P. — This  is  usually  obtained  by  adding  together  the 
watts  lost  in  the  armature  copper  and  iron.  The  value  of  the  iron- 
loss  watts  has  been  dealt  with  on  pp.  29,  30,  and  the  total  copper- 
losses  are  easily  obtained  from  the  value  of  the  armature  resistance. 

*  Cf .  Method  5,  p.  82. 


TEMPERATURE-RISE— ARMATURES 


81 


Professor  Arnold  *  has,  however,  pointed  out  that  the  copper-losses 
taking  place  in  the  end-connections  cannot  properly  be  considered 
as  heating  the  armature- core,  and  there  is  some  justification  for  this 
view,  as  results  testify.  Thus,  in  computing  the  armature-heating 
by  his  method  the  whole  of  the  iron-losses  are  added  to  those  copper- 
losses  which  take  place  in  the  copper  actually  lying  in  or  on  the  core. 

In  criticism  of  this  system,  it  may  be  remarked  that  much  expends 
upon  the  ratio  of  iron-losses  to  copper-losses,  and  upon  the  ratio  of 
copper-losses  due  to  the  copper  in  the  slots  to  that  occurring  in  the 
connections.  These  factors  depend  again  upon  various  conditions, 
notably  the  number  of  poles ;  and  in  any  case  the  method  hardly  lends 
itself  to  preliminary  calculations. 

The  Value  of  A. — The  number  of  ways  of  calculating  A  is  very 
large,  each  designer  having  his  own  system.  We  may  distinguish 
two. 

(1)  That  most  commonly  adopted,  in  which 

A  =  7r(diameter  of  armature  x  length  over  end-connections). 

(2)  That  which  takes  into  consideration  the  ventilating  spaces, 
etc.,/  existing  through  the  core.     This  value  of  A  is  best  seen  by 


FIG.  4.6. — COOLING  SURFACE  OF  AEMATDEE.    METHOD  8. 

reference  to  Fig.  46,  in  which  those  surfaces  marked  with  thick  black 
lines  are  considered  as  effective  and  are  added  together  to  give  A.  f 

Values  of  constants  a  and  b. 

For  method  (1),  the  value  of  b  may  be  taken  at  0'0005.  For 
well-ventilated  machines  a  then  varies  between  45  and  20.  The 
former  value  is  to  be  taken  for  the  smaller  machines,  as,  for  instance, 
those  with  armatures  about  12  to  18  inches  diameter,  where  the  hole 
through  the  core  is  largely  blocked  by  shaft  and  spider.  It  should 
be  added  that  the  figures  given  by  Hobart,  t  calculated  on  this  basis, 
would  make  the  value  of  a  higher ;  but  the  author  finds  the  above 
reliable. 

For  method  (2),  b  =  0'0005  and  a  varies  between  45  and  90  for 

*  "  Die  Gleschstrommachme,"  vol.  i.  p.  527. 

t  Cf.  Page  and  Hiss,  Journal  I.E.E.,  vol.  xxxix.  p.  576 ;  also  Arnold,  toe.  cit. 

I  "  Electric  Motors,"  Whittaker  &  Co.,  1st  Edition. 


82      CONTINUOUS   CURRENT   MACHINE   DESIGN 

well-ventilated  armatures,  the  higher  figure  being  for  very  small 
machines.  In  criticism  of  this  system  it  should  be  said  that  much 
depends  upon  the  width  of  the  ducts  through  the  stampings,  which 
vary  considerably  with  different  makes,  and  in  some  cases  are  so 
narrow  as  to  be  practically  useless. 

The  methods  just  given  are  a  fair  summary  of  those  commonly 
in  use,  and  will  be  found  in  most  cases  to  compare  well  with  one 
another.  There  is,  however,  no  alternative  but  for  the  designer 
to  determine  for  himself  which  method  is  most  reliable  for  the 
particular  type  of  machine  he  is  at  work  upon,  and  by  careful 
tabulation  to  build  up  for  himself  a  series  of  consistent  approximate 
data.  Especially  is  this  the  case  when  a  fan  is  added  inside  the 
motor  (as  Fig.  124);  though  roughly  it  is  found  that  such  a  fan 
decreases  a  by  5  %  to  10  %. 

There  are  other  methods  not  entirely  dependent  upon  the  formula, 
two  of  which  deserve  attention. 

Method  3  consists  in  expressing  the  number  of  watts  that  an 
armature  will  dissipate  as  a  function  of  the  product  (core-diameter2 
X  core-length)  for  each  peripheral  speed.  It  is  evident,  since  the 
cooling  surface  is  not  directly  proportional  to  the  quantity  (diameter2 
X  length),  that  such  a  relationship  must  be  determined  for  each 
particular  type  of  armature.  Indeed,  if  the  relationship  between 
core-diameter  and  length  be  assumed  or  known,  the  desired  curves 
may  be  deduced  from  methods  (1)  or  (2).  The  necessity  for 
knowing  the  length  renders  the  system,  unsatisfactory,  but  it  is 
extremely  handy  in  another  way ;  for  if  the  number  of  watts  to  be 
dissipated  by  the  armature  is  known  (and  this  is  usually  obtainable 
from  the  output  and  efficiency),  the  product  (diameter2  x  length  of 
the  core)  is  also  known  for  each  peripheral  speed.  Further,  since  the 
relationship  between  diameter  and  length  has  been  shown  to  depend 
on  the  number  of  poles  (p.  20),  the  dimensions  of  the  armature-core 
as  limited  by  temperature  are  known  for  a  given  output  and  speed 
and  number  of  poles.  Figs.  4^  and  48  show  values  for  the  above 
relationship  as  given  by  Macfarlane  and  Burge.* 

Method  4. — This  method,  due  to  Senstius,f  is  here  given  more 
because  of  its  simplicity  and  originality  than  because  of  its  general 
use,  though  it  certainly  leads  quickly  to  useful  limits.  The  system 
is  founded  on  an  assumption  akin  to  that  made  by  Arnold,  viz.  that 
the  heating  of  the  end-connections  is  practically  independent  of  that 
of  the  core.  Arnold,  in  general,  deals  with  the  core ;  while  Senstius 
considers  that  by  proper  ventilation,  if  the  frequency  do  not  exceed 
30,  the  core  can  always  be  kept  cool ;  and  that  the  limit  is  imposed 
by  the  end-connections,  for  which  he  gives  the  following  rule : — 

*  Journal  I.E.E.,  vol.  xlii.  pp.  239-240. 
t  Proc.  Amer.  I.E.E.,  vol.  xxiv.  p.  422. 


TEMPERATURE-RISE— ARMATURES  83 

"For  peripheral  speeds  ranging  from  1500  feet  per  minute  to 


0  1000  2000  3000  4000  5000  6000  7000  8000  9000  10000 
COBE  D2  L  VALUES  (C0.  INCHES). 

FIG.  47. — PERMISSIBLE  KILOWATTS  Loss  IN  ARMATURE — As  A  FUNCTION 
OF  THE  CORE  SIZE  FOR  SMALL  MACHINES. 


10000  20000  30000  40000  50000  60000  70000  80000  90000  100000 

CORE  D3  L  VALUES  (Cc.  INCHES). 

FIG.  48.  PERMISSIBLE  KILOWATTS  Loss  IN  ARMATURE — As  A  FUNCTION 
OF  THE  CORE  SIZE  FOR  LARGE  MACHINES. 

7000  feet  per  minute,  for  a  coil-depth  (not  slot-depth)  of  1/25  inch, 


84      CONTINUOUS   CURRENT   MACHINE   DESIGN 

and  a  temperature-rise  of  the  end-connections  not  exceeding  25°  C.,  the 
number  of  ampere-turns  per  inch  of  armature-circumference  varies 
as  a  straight  line  from  260  ampere-turns  per  inch  to  400  ampere- 
turns  per  inch."  Presumably,  Senstius  means  in  the  above  "coil- 
depth  "  not  exceeding  1*25  inch,  as  he  uses  it  himself  in  that  way. 

Comparison  of  Methods. — The  results  shown  in  Figs.  47  and 
48  may  be  deduced  direct  from  the  formulse  of  methods  either  (1)  or 
(2),  provided  that  a  relationship  between  diameter  and  length  of 
armature  is  assumed.  Thus,  suppose  from  p.  20  we  take  the  ratio  for 
poles,  viz. — 

diameter  of  armature      length  of  core 
number  of  poles  T5A 

Then  in  applying  method  (1)  we  need  but  an  approximate  relation- 
ship between  length  of  core  and  gross  armature  length ;  which  may 
be  written — 

armature-lenffthinclud-1  ,       ,1,0      -,      .,  i 

ing  end-connections    }  =  "ore-length  +  f  pole  pitch 

=  core-length  +  f  TT  .  — 

=  core-length  +  2-35   °^£& 
=  2*36  X  core-length  nearly. 

For  square  poles,  in  which  the  figure  1'5  becomes  1/2  (p.  20), 
we  have,  armature-length  including  end-connections  =  2*8  X  core- 
length. 

Then  in  the  formula  T  =  -?  -       a 


A  1  +  bv 
ifT  =  40°C. 


For  round  poles  — 
for  square  poles  — 


-P.  P 

=     ' 


Multiplying  both   sides   of   the   above   equations   by   D   gives   an 
immediate  comparison  with  method  3. 

Example.  —  As  a  concrete  case  for  comparative  purposes,  we  may 
check  the  machine  shown  in  Fig.  24  by,  say,  methods  1,  2,  and  3. 
We  will  assume  a  peripheral  speed  of  2500  feet  per  minute,  corre- 
sponding to  about  400  E.P.M. 


TEMPERATURE-RISE— ARMATURES  85 

As  the  machine  has  4  poles 

Length  over  end-connections  =  14"  +  f •  •  — V— "  =  28  J  inches 

Cooling  surface  (method  1)  =  2130  square  inches 

a  =  27  say 
so  that  P  =  7150 

Cooling  surface  (method  2)  =  3700  square  inches 

a  =  54 
so  that  P  =  6200 

Again,  from  Fig.  47,  method  3 — 

Diameter2  X  length  =  8060 
P  =  7800 

The  third  method  thus  gives  a  result  approximating  to  method  (1) ; 
while  method  (2)  gives  a  much  lower  value.  This  is  because  the 
number  of  ventilating  spaces  for  this  length  of  armature  is  small. 

With  three  ventilating  spaces,  which  would  be  more  usual, 
method  (2)  gives — 

P  =  7500  watts 

So  that  this  is  a  good  check  on  the  others,  and  probably  the  most 
satisfactory  form  for  final  calculations. 

General  Dimensions  derived  from  Heating  Formulae. — 
From  the  relationships  detailed  above,  it  is  evident  that  the  necessary 
dimensions  of  the  armature  for  a  given  output  can  with  some 
accuracy  be  predicted;  the  more  so  if  the  peripheral  speed  be 
approximately  determined.  So  obvious  is  this  that  emphasis  is 
hardly  necessary.  However,  for  the  sake  of  clearness,  the  example 
which  has  already  been  developed  on  p.  23  may  be  taken.  It  was 
there  shown  that  by  the  formulae  which  ordinarily  limit  the 
machine  dimensions,  a  200  K.W.  400  r.p.m.  generator  would  require  an 
armature  with  a  D2L  value  =  10,000.  If  we  assume  again  an 
efficiency  of  93  per  cent,  at  f  full  load,  the  variable  losses  will  be 
about  5'25  K.W.  at  that  load,  or  9'3  K.W.  at  full  load.  A  preliminary 
estimate  of  the  iron-losses,  such  as  that  on  p.  30,  shows  that  these 
will  amount  to  about  2000  watts.  From  the  variable  losses  must  be 
subtracted  the  loss  in  compounding  coils,  say  f  per  cent,  or  600 
watts ;  and  the  commutator  C2E  loss.  The  latter  has  not  yet  been 
considered,  but  we  may  estimate  it  at  1  K.W.  The  balance  then, 
viz.  (9-3  +  2)  -  (1  +  0'6)  =  9-7  K.W.,  has  to  be  radiated  by  the 
armature.  From  method  (3),  Fig.  48,  assuming  a  peripheral  speed 
of  about  3000  feet  per  minute,  we  shall  require  an  armature  with  a 
D2L  value  of  about  9000. 

From  method  (1)  T  =  ,    ,\    .  - 
1  -f  bv    A 


86      CONTINUOUS   CURRENT   MACHINE   DESIGN 

Now,  from  p.  84,  A  =  -rrDL  X  2'36 

Inserting   this   value,    and    also    a  =  27,    P  =  9700,    T  =  40°, 
6  =  0-0005,  v  =  3000,  we  obtain  DL  =  300. 

Whence  for  a  4-pole  machine  in  which  the  poles  are  circular,  and 


we  get  D2  =  710,  and  D  =  27"  nearly 

Also,  since  L  =  11-5,     D2L  =  8100 

which  compares  fairly  well  with  method  3. 

As  a  further  test,  try  the  method  of  Senstius. 

For  25°  C.,  at  3000  feet  per  minute,  the  ampere-turns  per  inch 
will  be,  according  to  the  rule  given  — 

3000  -  1500    400  -  260 
f  7000  -  1500  '       ~T~ 
For  40°  C.,  then,  they  will  be— 

•Y/lf  X  298  =  377  ampere-turns  per  inch 
or  ampere-  conductors  per  inch  =  754 

Inserting  this  value  in  the  equation  on  p.  22,  viz. 

T)2j  .  60*8  x  pole-pitch  x  107  watts 

"~  density  at  face  X  754  x  pole-arc      E.P.M] 

60-8  x  500  X  107 
=  55,000  x  754  x  0-7  =    l°'°C 

which  is  somewhat  higher  than  the  result  given  by  methods  1  or  2, 
probably  because  the  "  coil-depth  "  will  not  approach  the  limit  of 
Senstius,  viz.  1|  inch.  Yet  allowing  for  this,  and  considering  how 
different  the  methods  are,  the  agreement  must  be  considered  very 
good,  as  providing  a  starting-point  for  a  design  limited  only  by 
heating. 

Commutators. 

Losses  causing  Heat.  —  These  may  be  divided  into  (a)  electrical, 
(&)  mechanical. 

The  former  comprise  the  losses  due  to  resistance  of  the  bars,  and 
of  the  contact  between  the  bars  and  the  brushes.  There  is  also  a 
small  eddy-current  loss  in  the  commutator  section  itself  due  to  the 
changes  which  take  place  in  the  current  it  is  called  upon  to  carry. 
Of  these  losses,  that  due  to  the  resistance  of  the  brush  contact  is  by 
far  the  largest,  and  the  methods  of  calculating  it,  together  with  some 
account  of  the  factors  upon  which  it  depends,  are  given  under  the 
heading  of  "  Dimensions  of  Commutators  "  on  p.  133. 

The  mechanical  loss  is  that  due  to  the  friction  of  the  brushes 
upon  the  commutator.  This  is  dealt  with  on  p.  133. 

The  construction  of  the  commutator  should  always  be  such  as  to 


commutator  resistance-  and  friction-losses 


TEMPERATURE-RISE— ARMATURES  87 

provide  as  much  cooling  surface  as  possible.  Examples  of  modern 
designs  are  given  in  Eigs.  3  and  112,  from  which  the  methods  of 
providing  ventilation  will  be  apparent. 

For  any  construction,  however,  the  heating  of  the  commutator  is 
usually  estimated  from  the  external  cylindrical  cooling  surface  only. 
With  good  ventilation  for  40°  C.  rise,  the  watts  which  this  surface  will 
dissipate  per  square  inch  =  3  to  5 ;  with  poorer  ventilation,  2  to  3 
watts  per  square  inch. 

On  the  average  then 

area  of  commutator  ex- 
ternal cylindrical  sur- 
face in  square  inches 
as  limited  by  tempe- 
rature rise 

The  length  of  the  external  cylindrical  surface  is  measured  from 
the  outside  of  the  commutator- segment  to  the  riser,  and  excludes 
the  length  occupied  by  the  risers  themselves. 

Naturally,  the  value  of  the  constant  to  be  adopted  in  the  above 
formula  is  dependent  upon  the  peripheral  speed  of  the  commutator- 
face.  This,  in  ordinary  machine  design,  rarely  exceeds  3600  feet  per 
minute,  as  chattering  of  the  brushes  is  liable  to  occur  at  higher  speeds. 

We  have  then  a  rough  limit  for  the  size  of  the  commutator-face, 
and  when  the  diameter  is  not  limited  by  peripheral  speed  it  is  usually 
determined  by  the  number  of  segments,  each  of  which  with  its  appro- 
priate insulation  is  rarely  less  than  fy  inch  thick  at  the  commutator- 
lace.  The  application  of  the  above  figures  is  so  patent  as  to  need  in 
this  place  no  concrete  example. 

Heating  of  Totally  Enclosed  Motors. — The  temperature-rise 
of  totally  enclosed  motors  is  best  estimated  from  the  total  radiating 
surface  which  the  complete  machine  offers.  The  method  of  calculat- 
ing this  surface  varies  with  different  designers,  but  in  general  it  is 
taken  to  be  the  total  external  surface  of  the  motor.  On  account  of 
the  fact  that  the  bearings  sometimes  heat  rather  more  than  any  other 
part,  some  designers  reckon  the  exposed  radiating  surface  of  the 
bearings  twice  over.  Within  ordinary  ranges  of  motor  designs,  as 
from  5  to  50  H.P,,  a  temperature-rise  of  50°  C.  will  be  reached 
when  from  0*4  to  0*6  watt  is  dissipated  for  each  square  inch  of 
external  surface.  An  average  figure  would  be  0'5.  Artificial  increase 
of  the  external  surface  by  means  of  ribs  or  similar  projections  will 
modify  the  above  figure  ;  and  it  may  be  said  in  general  that  it  is  best 
to  collect,  from  experimental  data  on  the  particular  type  of  machine 
in  hand,  a  series  of  results  which  can  be  put  into  curve  form  for 
future  use.  This  is  especially  necessary  in  cases  where  machines  are 
to  be  short-rated.  It  may  be  added  that  fans  in  T.E.  motors  are 
useless  unless  ribs  be  provided  inside  the  case  as  well  as  outside. 


88      CONTINUOUS   CURRENT   MACHINE   DESIGN 

Such  a  series  is  shown  for  a  particular  style  in  Fig.  49,  and  the 
values  are  fairly  typical.  On  the  curves  the  figures  ?,,  f ,  etc.,  refer 
to  the  hours  at  which  the  machines  are  rated  for  a  rise  of  50°  C.,  and 
the  dotted  lines  AB  and  CD  represent  two  sizes  of  machine. 
Thus  the  point  A  shows  that  the  machine  represented  by  the  dotted 
line  AB  will  stand  a  load  of  72  watts  per  revolution  per  minute  for 
a  rise  of  50°  C.  in  three  hours,  and  that  the  watts  per  square  inch  of 
radiating  surface  are  then  0*75.  Having  a  series  of  limiting  values 


1-6 


1-4 


1-2 


0-6 


0-4 


0-2 


100 


120 


140 


160 


0  20  40  (30  80 

INPUT.    AVATTS  PER 
FIG.  49.— HEATING  OF  TOTALLY  ENCLOSED  MOTORS. 

like  these,  it  is  easily  possible  to  interpolate  for  any  new  intermediate 
size.  Thus,  suppose  a  machine  be  required  capable  of  giving  9000 
watts  at  300  revolutions  per  minute ;  i.e.  30  watts  per  revolution  per 
minute.  From  the  curve,  it  is  evident  that  for  a  three-hour  rating 
each  square  inch  of  the  carcase  will  dissipate  0*53  watt.  If  the 
efficiency  of  the  machine  be  estimated  at  80  per  cent.,  the  input  will 
be  11,250  watts,  and  the  losses  2250  watts ;  so  that  the  external 

2250 
radiating  surface  required  is  -^  >Q  =  4250  square  inches. 


CHAPTER   VIII 
ARMATURE  WINDINGS 

IT  would  not  be  possible,  nor  is  it  desirable,  in  a  work  of  this  scope 
to  describe  in  detail  either  all  the  elementary  principles  of  armature 
winding  on  the  one  hand,  or  all  the  various  forms  into  which  those 
windings  have  ultimately  developed  on  the  other.  It  should  be 
sufficient  to  indicate  in  a  general  way  the  principles  underlying  all 
the  usual  forms  of  armature  winding,  and  to  set  down  in  some  detail 
the  rules  governing  the  application  and  form  of  those  windings  which 
are  now  most  commonly  met  with.  It  is  supposed  that  the  reader  is 
familiar  with  the  rudiments  of  armature  winding,  and  the  outline 
now  to  be  given  must  be  filled  in  from  his  previous  knowledge  or 
subsequent  experience. 

Types  of  Armature  Winding. — There  are  two  general  types  of 
armature  winding — the  open-coil  and  the  closed-coil.  In  the  first  type 
current  is  taken  from  each  coil  only  at  the  time  when  it  is  developing 
its  maximum  E.M.F.,  all  the  other  coils  being  at  that  moment  cut 
out  entirely.  The  open-coil  armature  is  only  used  for  series  arc 
lighting,  where  a  constant  current  with  a  high  potential  difference  is 
required ;  the  advantage  of  the  system  lies  in  having  no  difference  of 
potential  between  adjacent  commutator-bars  connected  to  coils  not 
simultaneously  in  circuit.  This  type  of  armature  is  not  much  used, 
having  been  replaced  almost  entirely  by  the  second  type. 

Closed  Coil  Armatures. — The  closed-coil  armature,  apart  from 
the  commutator,  forms  an  endless  winding,  so  that  when  we  imagine 
the  commutator  and  core  dissolved  away  without  otherwise  dis- 
turbing the  winding,  on  pulling  the  latter  it  would  be  found  to 
consist  of  one  or  more  endless  bands.  Such  a  winding  is  said  to  be 
"  re-entrant,"  because  it  closes  upon  itself ;  *  one  winding  returning 
on  itself  is  said  to  be  singly  re-entrant,  whereas  a  winding  formed 
of  two  or  more  independent  endless  bands,  each  closing  upon  itself, 
is  said  to  be  multiply  re-entrant.  Thus  in  a  "  doubly  re-entrant " 

*  The  notation  here  followed  is  that  of  Parshall  &  Hobart ;  see  also  Cramp's 
"  Armature  Windings  of  the  Closed-circuit  Type,"  Biggs  &  Sons. 


90      CONTINUOUS   CURRENT   MACHINE   DESIGN 

armature  winding  we  have  two  separate  windings  each  closing  upon 
itself.  These  short  definitions  are  here  inserted  on  account  of  the 
confusion  that  has  arisen  in  the  use  of  these  terms. 

A  closed-coil  armature  can  have  no  less  than  two  paths  in 
parallel  through  it.  Each  of  these  will  have  the  same  number 
of  turns,  and  the  current  entering  one  brush  will  divide  equally 
through  the  two  halves  to  unite  again  at  the  other  brush.  There 
may  be  more  than  two  parallel  paths  for  a  "  singly  re-entrant  " 
winding,  as  we  shall  see  later;  and,  of  course,  there  will  be  more 
than  two  parallel  paths  for  a  "  multiply  re-entrant  "  winding. 

Closed-coil  armature  windings  can  be 
divided  into  two  classes,  ring  winding  and 
drum  winding. 

Elementary  Bi-polar  Ring.  —  In  order 
to  make  subsequent  explanations  more  clear, 
we  must  here  refer  to  this  now  practically 
obsolete  type.  The  simple  Gramme  ring 
armature  consists  of  a  series  of  spirals  of 
wire  wound  about  an  annular  core  in  regular 
order  (Fig.  50),  the  last  turn  of  the  last 
spiral  being  connected  to  the  beginning  of 
the  first.  At  points  equally  spaced  around 
the  winding  connections  are  made  to  com- 
mutator segments  as  shown  in  Fig.  50. 
In  actual  practice  the  end  of  each  coil 
would  be  brought  down  to  the  commutator 
segment,  and  there  connected  to  the  begin- 
ning of  the  next  coil,  thus  avoiding  the 
FIG.  50.—  BI-POLAR  BING  large  number  of  soldered  T  joints.  With 
ARMATURE.  two  brushes  at  opposite  ends  of  a  neutral 

diameter  Bb  B2,  the  winding  is  divided  into 

parallel  halves.  If  a  =  cross-section  of  the  wire  in  square 
inches,  and  I'  =  total  length  of  wire  in  inches,  then  the  resistance 

I' 

p.  g 
of  each  half  of  the  winding  is  -  >  where  p  =  the  specific  resistance 

of  copper  at  some  definite  temperature.  Hence  the  armature 
resistance  Ra  is  — 

r 


Turns  per  Segment.  —  Instead  of  one  turn  per  commutator 
segment,  as  shown  in  Fig.  50,  there  may  be  as  many  turns 
between  one  segment  and  the  next  as  is  consistent  with  sparkless 


ARMATURE    WINDINGS  91 

commutation*  (see  Fig.  51);  the  author  has  had  instances  of  as 
many  as  80  turns  in  each  armature  coil,  i.e.  between  one  commutator 
segment  and  the  next. 

Multipolar  Simple  Ring- Winding. — The  ring-armature  in 
Fig.  50  can  be  employed  for  a  machine  with  four  poles  (Fig.  51) ; 
and,  in  general,  if  the  armature  has  a  sufficiently  large  number  of 
spirals,  the  same  winding  can  be  used  with  any  number  of  poles. 

The  arrows  in  Fig.  51  show  the  relative  directions  of  the  various 
induced  E.M.F.'s.  In  order  that  currents  may  naturally  flow 
under  the  influence  of  these  E.M.F/s,  it  is  obviously  necessary  that 
collection  should  take  place  at  those  places  where  each  series  of 
induced  E.M.F.'s  meets  its  neighbouring  series.  These  places  are 
often  called  "neutral  points" 
(cf.  p.  52),  because  no  E.M.F. 
is  generated  in  coils  which  lie 
there,  since  such  coils  are  under 
the  influence  of  no  field. 

The  number  of  neutral 
points  with  four  poles  is  four, 
and  for  electrical  balance  we 
require  four  brushes,  alternate 
brushes  being  of  the  same 
polarity  and  connected  to  one 
another.  The  number  of  cir- 
cuits in  the  armature  is  the 
same  as  the  number  of  poles. 
The  addition  of  another  pair 

of  poles,  if  that  were  possible,  FIG.  51. 

would  necessitate  another  pair 

of  brushes,  and  would  add  thereby  another  pair  of  armature  sections, 
and  so  on.  These  sections  or  circuits  are  put  in  parallel  at  the 
brushes,  and  as  each  section  has  the  same  current-carrying  capacity, 
the  current  that  can  be  taken  from  the  machine  is  proportional  to 
the  number  of  poles.  Such  windings  in  which  the  minimum  number 
of  circuits  possible  is  equal  to  the  number  of  poles  are  designated 
multiple-circuit  windings. 

Pitch. — The  distance  from  spiral  to  spiral  in  Figs.  50  or  51,  i.e. 

~  of  the  total  armature  circumference,  where  S  is  the  number  of 

spirals  or  of  coils,  as  the  case  may  be,  is  called  the  distance-pitch  of 
the  spirals  or  coils.  If,  as  in  Fig.  50,  the  number  of  coils  is  24,  the 
distance-pitch  of  the  coils  is  J^-.  If  the  spirals  be  numbered  con- 
secutively around  the  armature,  the  difference  in  the  numbers  of  the 


See  p.  126,  on  reactance  voltage  of  the  short-circuited  coil. 


92       CONTINUOUS   CURRENT   MACHINE   DESIGN 

spirals  successively  connected  to  the  commutator  segments  is  called 
the  number  pitch,  or  simply  the  pitch.  In  Fig;  50  the  number  pitch 
of  the  spiral  is  1,  and  in  Fig.  51  the  number  pitch  of  the  coils  is  1. 

Commutator  Pitch. — If  the  connections  to  the  commutator  be 
numbered  successively,  then,  since  there  are  always  as  many  com- 
mutator sections  as  coils,  these  numbers  may  also  be  considered  as 
applying  to  the  coils.  But  the  order  of  the  ends  of  the  armature  coils 
may  not  be  the  same  as  the  order  of  these  connections ;  nor  need  they 
be  connected  to  neighbouring  segments.  For  this  reason  the  term  com- 
mutator pitch  is  used  to  denote  the  numerical  difference  between  the 
number  given  to  one  commutator  segment  and  that  given  to  the  seg- 
ment to  which  the  other  end  of  the  same  armature  coil  is  joined.  In 
the  ring  windings  of  Figs.  50  and  51,  and  generally  in  windings  of 
that  type,  the  two  ends  of  any  coil  are  connected  to  neighbouring 
sections,  so  that  the  commutator  pitch  is  unity. 

Drum  Windings. — From  the  preceding  summary,  it  is  clear  that 
each  turn  or  spiral  of  a  ring  armature  consists  of  an  active  part  lying 
on  the  outside  of  the  core,  which  we  shall  hereafter  refer  to  as  the 
"surface  conductor,"  and  an  inactive  part  forming  the  connection 
between  one  surface  conductor  and  the  next,  of  which  a  great  portion 
lies  inside  the  core.  The  essential  distinction  between  the  ring  and 
the  drum  winding  consists  in  the  fact  that  the  whole  of  the  spiral  is 
in  the  latter  type  placed  on  the  outside  of  the  armature,  so  that  the 
portion  which  was  within  the  core  now  forms  a  second  active  part  or 
surface  conductor,  while  the  connections  between  the  two  project 
from  the  core  ends,  as  shown  in  Figs.  3  and  71.  Following  out  this 
idea,  the  author  has  in  another  place  *  shown  how  from  the  ring,  the 
drum  winding  may  be  developed  and  understood.  Here  it  is  suffi- 
cient to  indicate  the  line  of  reasoning  by  calling  attention  to  two 
important  points.  First,  since  in  the  ring  there  is  an  inner  wire  cor- 
responding to  each  surface  conductor,  the  number  of  conductors  on  the 
surface  of  the  corresponding  drum  will  be  twice  what  it  was  in  the 
original  ring.  Consequently,  whether  the  ring  were  wound  with  an 
odd  or  even  number  of  spirals,  the  number  of  conductors  on  the 
drum  becomes  even. 

Secondly,  in  the  case  of  any  spiral  on  the  ring,  the  fact  that  the 
inner  wire  passes  back  through  the  armature  causes  the  current  to 
be  apparently  opposite  in  direction  to  that  carried  by  the  conductor 
upon  the  surface.  Therefore,  if  the  inner  wire  of  the  ring  is  to  be 
placed  upon  the  outside  of  the  armature,  to  become  useful,  and  if  it 
is  to  be  directly  connected  to  the  original  surface  conductor,  it  must 
lie  in  a  field  of  opposite  polarity  to  that  in  which  the  original 
conductor  lay. 

*  "  Armature  Windings  of  the  Closed-circuit  Type." 


ARMATURE   WINDINGS  93 

In  Fig.  52  we  have  a  bipolar  drum  winding  of  ten  turns  composed 
in  this  way.  The  Roman  numbers  indicate  the  turns  :  for  instance, 
I  is  the  "  old  "  conductor,  and  I'  the  "  new  "  conductor.  Starting  at 
I,  the  winding  passes  across  to  I'  and  thence  to  II,  and  after  that  to  II', 
and  so  on.  The  connections  to  the  commutator  are  at  the  junction 
of  I  and  I',  II  and  II',  etc.  If  the  conductors  be  numbered  succes- 
sively, as  indicated  by  the  Arabic  numerals,  we  note  that  the  "  old  " 
conductors  are  odd  and  the  "new"  even.  The  difference  in  the 
numbers  of  I  and  I'  is  odd,  and  constitutes  what  is  termed  the  front 
or  forward*  pitch  (yj).  The  difference  in  the  numbers  of  I'  and  II 
is  also  odd,  and  is  called  the  backward  pitch  (yb).  The  forward  and 
backward  pitches  are  11  and  9  respectively  in  this  case. 

It  is  seen  that  for  this  simple  drum  winding  yf  —  y^  —  2,  and 
obviously  the  total  number  of  surface  conductors  is  even.  Since  the 


FIG.  52. 

number  of  segments  of  the  commutator  is  equal  to  the  number  of 
coils,  each  of  which  in  this  case  consists  of  one  turn,  the  number  of 
segments  of  this  simple  drum  winding  is  half  the  number  of  surface 
conductors. 

The  commutator  pitch  is  unity.  The  brushes  are  placed  on  the 
segments  connected  to  the  conductors  lying  in  the  neutral  position 
(i.e.  lying  between  the  poles) .  The  formula  for  the  armature  resistance 
is  exactly  the  same  as  for  the  ring  armature. 

Progressive  and  Retrogressive  Windings. — In  the  preceding 
example,  had  the  backward  pitch  been  greater  than  the  forward  pitch 
by  2  (i.e.  yb  —  yf  =  2),  then  the  winding  would  have  been  retro- 
gressive, but  the  scheme  is  practically  the  same  as  the  winding  shown, 
which  is  said  to  be  progressive.  There  is  this  difference,  however, 
that  the  E.M.F.  of  the  brushes  is  reversed,  and  therefore,  in  the  case 

*  Note  that  the  forward  pitch  throughout  this  work  is  the  number-pitch  of  the 
conductors  at  the  end  remote  from  the  commutator. 


94      CONTINUOUS   CURRENT   MACHINE   DESIGN 

of  a  motor,  the  armature  would  rotate  in  the  opposite  direction  for 
the  same  polarity  of  the  fields.  A  bipolar  progressive  winding,  then, 
is  one  in  which  the  pitch  at  the  end  remote  from  the  commutator  is 
greater  than  that  at  the  commutator  end,  the  former  being  reckoned 
in  the  clockwise  direction  when  the  armature  is  viewed  from  the 
commutator  end. 

Multipolar  Drum  Windings. — Drum  windings  for  armatures 
of  multipolar  machines  are  divided  into  two  general  classes — 

(a)  Multiple-circuit  or  lap-wound. 

(b)  Two-circuit  or  wave-wound. 

The  distinction  between  these  classes  lies  in  the  fact  that  in  the 
former  the  turns  "  lap  back/'  while  in  the  latter  the  coils  progress 
from  pole  to  pole.  This  will  be  seen  more  clearly  from  the  follow- 
ing diagrams. 

(a)  The  simple  multiple-circuit  or  lap  winding. 

It  has  been  pointed  out  that  in  the  bipolar  drum  winding, 
a  surface  conductor  under  a  north  pole  must  be  connected  to  one 
under  a  south  pole,  and  the  same  holds  good  for  the  multi- 
polar  case.  From  an  electrical  point  of  view  the  poles  need  not  be 
adjacent,  but  for  geometrical  reasons,  because  the  system  will  then 
require  a  minimum  length  of  wire,  the  conductors  under  adjacent 
poles  are  connected  together.  As  far  as  possible,  those  lying  under 
similar  portions  of  the  poles  should  be  connected,  as  this  tends  to 
yield  the  greatest  E.M.F.  for  a  given  flux.  The  total  number  of 
conductors  divided  by  the  number  of  poles  is  termed  the  pole-pitch 
of  the  winding ;  for  it  is  the  distance,  expressed  in  terms  of  con- 
ductors, between  the  centres  of  two  adjacent  poles.  If  the  for- 
ward pitch  of  the  conductors  be  very  much  less  or  greater  than 
the  pole-pitch,  both  the  conductors  of  a  turn  will  come  under  the 
influence  of  one  polarity  and  give  zero  E.M.F.  for  that  turn.  Never- 
theless, windings  with  a  pitch  less  than  the  pole-pitch  have  been 
suggested  for  the  reasons  referred  to  under  the  heading  "  Chord 
Winding"  below.  The  forward  pitch  yf  is  usually  taken  equal  or 
slightly  less  than  the  pole-pitch,  and  must  be  odd.  The  backward 
pitch  is  for  a  progressive  winding  =  yf  —  2,  and  for  a  retrogressive 
.winding  =  yf  +  2,  and  must  necessarily  be  also  odd. 

Moreover,  if  the  direction  of  the  E.M.F.'s  in  the  conductors  of 
these  drum  armatures  be  compared  with  those  of  the  ring  arma- 
tures (as  indicated  by  the  arrow-heads  in  Fig.  51),  it  will  be 
found  that  the  winding  is  naturally  divided  into  as  many  circuits 
as  there  are  poles,  and  that  in  any  two  neighbouring  circuits  the 
E.M.F.'s  (and  consequently  the  currents)  must  oppose  one  another. 
Therefore  for  effective  collection  of  these  currents  brushes  must  be 
placed  upon  the  commutator  bars  connected  to  the  neutral  conductors 
in  which  these  currents  would  naturally  meet.  This  results  in  as 


ARMATURE   WINDINGS 


95 


many  rows  of  brushes  on  the  commutator  as  the  machine  has  field- 
poles,  alternate  rows  being  connected  together  to  form  one  pole  of  the 
machine. 

For  example,  in  Fig.  53  the  number  of  surface  conductors  is  24, 
and  of  poles  4 ;  hence  the  pole-pitch  of  the  windings  =  6. 

Choosing  an  odd  number  for  the  forward  pitch — 
we  have  y/  =  7 
so  that  ?/b  =  7  —  2  =  5  for  a  progressive  winding. 

In  the  figure,  one  set  of  connections,  if  carefully  followed,  will 
show  the  character  of  the  simple  multiple  circuit  or  "  lap  "  winding 
and  its  progression.  The  position  and  the  number  of  the  rows  of 


FIG.  53. — SIMPLE  MULTIPOLAB  DEUM  WINDING. 

brushes  are  both  clearly  indicated ;  there  are  12  commutator  bars,  and 
the  commutator  pitch  is  1. 

Conventional  Winding  Table. — It  is  convenient  to  express  the 
connections  in  a  conventional  winding  table.  This,  for  the  winding 
we  have  just  discussed,  is  as  follows : — 

1~8_3~~10_5— 12_7~  14    9—16,  etc. 

The  paths  of  the  currents  through  the  armature  for  the  particular 
brush  position  shown  in  the  figure  will' be — 

/  5, 12,  7,  14x 

+  Terminal     /  +  Brusn  1\o    1    fi  2V  ~  Brush  2\     -Terminal 
of          /  '     '     '  N  of 


machine 


,  24,  19, 


-  Brush  4/ 


machine 


96      CONTINUOUS   CURRENT   MACHINE   DESIGN 

Development. — In  Fig.  54  the  winding  is  supposed  to  be  cut 
through  at  one  point,  removed  from  its  core,  and  laid  open  on  a  flat 


4123 
FIG.  54. — DEVELOPED  LAP-WINDING. 

surface.  This  is  termed  the  "  developed  winding "  or  "  develop- 
ment," and  indicates  clearly  the  characteristic  lapping  back,  besides 
showing  the  position  of  the  brushes.  The  characteristic  of  the  wind- 
ing is  emphasized  by  the  thickened  coil  or  turn. 

Chord  Winding. — If,  instead  of  taking  a  forward  pitch,  yf  about 
equal  to  the  pole  pitch,  we  choose  a  smaller  pitch  (still  giving  it  an 
odd  value),  we  shall  obtain  the  narrow  armature  coil  or  so-called 
"  chord  "  winding  of  Swinburne. 

The  advantage  of  the  "  chord  "  winding  is  that  the  currents  flow- 
ing in  the  armature  conductors  in  the  neutral  region  are  in  opposite 
directions,  so  that  their  magnetic  effect  is  zero,  and  therefore  they 
play  no  part  in  armature  reaction.  On  the  other  hand,  some  differen- 
tial action  tending  to  reduce  the  terminal  E.M.F.  often  results  (p.  94). 

Resistance  of  Drum  Winding. 

If  /'  =  total  length  of  wire  in  the  armature  winding  in  inches, 
a  =  cross-section  of  the  conductor  in  sq.  inches, 
p  =  specific  resistance  of  copper  at  specified  temperature, 
p  =  number  of  poles, 

I' 
p  .  — 

Then  resistance  of  armature  circuit  of  1  _       « 
a  multipolar  machine  J  "     p 

.'.  resistance  of  the  simplex  multiple!  =  1      a 
circuit  armature  J  ~~  p '  p 


ohms 


ARMATURE   WINDINGS 


97 


Duplex  Multiple-circuit  or  Lap  Windings. — The  forms  of 
winding  just  described  can  be  made  "  duplex,' '  "  triplex,"  etc.,  by 
placing  a  second  or  third  winding  upon  the  armature  connected  to 
commutator  segments,  which  are  regularly  interleaved  with  those  of 
the  first  winding ;  the  various  windings  are  then  placed  in  parallel 
at  the  commutator,  by  brushes  wide  enough  to  touch  at  least  as  many 
segments  as  there  are  windings  upon  the  armature.  Thus,  Fig.  55 
shows  a  ring  armature  upon  which  are  two  separate  and  distinct 
windings,  one  shown  full,  A,  B,  C,  etc.,  and  the  other  dotted,  marked 
A',  B',  C',  etc.  It  will  be  noticed  that  when  the  second  winding  is 
connected  down  to  the  commutator  in  the  same  way  as  the  first 


FIG.  55.— DUPLEX  EING  WINDING. 

winding,  its  segments  naturally  occur  alternately  interspaced  with 
those  of  the  first  winding,  hence  the  commutator  belonging  to  this 
form  will  have  twice  as  many  segments  as  the  corresponding  armature 
with  a  single  winding. 

Now,  if  each  brush  bearing  upon  the  commutator  be  made  so  wide 
that  it  never  touches  less  than  two  sections,  we  find  that  we  have, 
with  respect  to  these  brushes,  the  two  windings  on  the  armature 
continually  in  parallel. 

Object  of  a  Double  Winding. — The  sole  object  of  a  double  or 
duplex  winding  is  to  enable  the  armature  to  carry  a  large  current, 
and  to  split  up  this  heavy  current  into  sufficiently  small  parts  while 
it  is  being  commuted. 

H 


98      CONTINUOUS   CURRENT   MACHINE   DESIGN 

A  double  winding,  then,  in  general  only  supplies  a  method  where- 
by we  are  enabled  to  change  the  output  of  a  machine  by  simply 
altering  the  pitch  of  the  winding,  without  changing  either  the 
number  of  turns  upon  the  armature  or  the  number  of  commutator 
sections. 

Multiplex  Multiple  -  circuit  'Windings  (Multiple  Re- 
entrancy) :  Notation — In  Eig.  55,  instead  of  two  windings  in 
parallel,  three,  four,  or  any  desired  number  for  which  there  was  room 
might  have  been  wound.  In  the  illustration,  with  only  two  inde- 
pendent windings  the  armature  is  said  to  be  duplex  doubly  re- 
entrant ;  with  three  windings  it  is  said  to  be  triplex  triply  re-entrant, 


FIG.  56. — DOUBLY  RE-ENTRANT  LAP  WINDING. 

and   so  on.     The  following  is  the  notation   introduced  to  express 
this : —  > 

Simplex  winding,  o 

Duplex  doubly  re-entrant,  o  o      (=2  independent  windings) 

Triplex  triply  re-entrant,   o  o  o  (=3  independent  windings) 

and  so  on  for  any  number  of  independent  windings. 

Multiplex  Drum  Windings  of  Multiple  Re-entrancy. — Now, 
as  from  the  simplex  ring  winding  the  simplex  drum  winding  was 
developed,  so  from  the  multiplex  forms  of  the  ring  can  multiplex 
drum  windings  be  formed. 

In  Fig.  56  is  shown  a  4- pole  double-wound  or  duplex  drum 
winding.  The  two  windings  on  the  drum  are  entirely  separate,  and 


ARMATURE  WINDINGS  99 

the  adjacent  commutator  segments  belong  respectively  to  the  two 
windings.  The  black  dots  represent  the  conductors  of  one  wind- 
ing, and  the  circles  those  of  the  other.  Suppose  the  dots  to  be 
numbered  1,  2,  3,  4,  etc.,  and  the  circles  1',  2',  3',  4',  5',  etc.  Each 
winding  has  24  conductors,  so  that  the  pitches  for  each  winding  are 
yf  =  w/p  approximately,  where  w  =  No.  of  conductors  in  each 
winding. 

Since  y/  =  7,  an  odd  number 
and  2/^  =  5  (for  progressive  winding) 

The  scheme  for  the  windings  would  be — 

1_8~ 3_10~~5__12~7_14~~9,  etc. 
and 

l'_8'— 3'__10'~~ 5'_12'— 7'_14'~9',  etc. 

The  connections  belonging  to  one  winding  are  drawn  with  full 
lines,  and  those  of  the  second  winding  are  drawn  dotted.  The 
windings  are  put  in  parallel  with  each  other  by  means  of  the 
brushes,  each  brush  bearing  upon  not  less  than  two  segments  of 
the  commutator. 

Pitch  of  Multiplex  Lap  Windings  of  Multiple  Re- 
entrancy. — Since  the  number  of  conductors  in  each  winding  is 
even,  the  total  number  of  conductors  on  the  armature  is  divisible 
by  4,  i.e.  2  X  number  of  windings.  Had  there  been  m  windings,  the 
total  number  of  conductors  must,  if  each  winding  is  independent  and 
entirely  separate  from  the  others,  be  divisible  by  2m.  Thus  a 
winding  must,  in  the  first  place,  to  be  multiply  re-entrant,  have  its 
conductors  divisible  by  2m. 

If  the  conductors  be  numbered  consecutively  so  that  No.  24' 
becomes  No.  48,  we  see  that — 

y/=  14 

and  yb  =  10 

Since  y/  should  be  approximately  equal  to  the  pole-pitch,  this  value 
can  be  obtained  thus — 

Pole-pitch  =  ^  =  12 

.-.  yf  =  12  +  2  =  14 

The  difference  y/  —  y*  is  now  4 ;  that  is,  it  is  equal  to  2  x  number 
of  windings.  Had  three  windings  been  wound  triply  re-entrant, 
yf  -  yb  would  have  been  6,  and  generally  for  m  windings  m  times 
re-entrant — 

y/-y*  =  %m 

The  winding  scheme  for  the  duplex  winding  now  runs — 

1     15 5     19 ,  etc.  ...  1st  winding 

3— 17__7~~21  ...  2nd  winding 


ioo    CONTINUOUS   CURRENT   MACHINE   DESIGN 

For  a  4-pole  machine  with  228  conductors — 

yf  =  57  and  yb  =  53. 
The  winding  table  will  run — 

1     58 5~62_9~66,  etc.  ...  1st  winding 

3~60_7~64_11~68  .  .  .  2nd  winding 

The  commutator  pitch  yc  for  the  duplex  winding  is  evidently  2, 
and  generally  for  multiplex  lap  windings  yc  =  m. 

Circuits  through  the  Winding. — The  diagrams  show  that  the 
current  divides  at  each  brush  into  2m  paths,  where  m  =  number  of 
windings,  so  that  the  resistance  of  the  armature  becomes  1/m  times 
that  of  a  simplex  winding  (p.  96). 

Duplex  Winding  Singly  Re-entrant. — In  all  the  cases  so  far 
discussed  the  re-entrancy  has  been  equal  to  the  number  of  windings ; 


FIG.  57. 

there  is,  however,  another  class  of  winding,  certainly  of  little  import- 
ance, but  still  sometimes  to  be  met  with,  in  which  the  re-entrancy  is 
not  equal  to  the  number  of  windings,  i.e.  in  which  the  various 
windings  are  not  independent.  Two  examples  will  suffice  to  explain 
the  general  principle. 

It  is  possible,  in  the  case  of  a  ring  armature,  to  set  out  the  spirals 
with  such  a  pitch  that  the  winding  naturally  continues  twice  or 
more  times  around  the  armature  still  finally  closing  on  itself.  This 
is  exemplified  in  Fig.  57,  which  has  31  spirals  upon  it,  with  a 


ARMATURE  WINDINGS'  ;ioi 

regular  distance-pitch  ^-  of  the  circumference.  It  is  naturally  a  duplex 
winding,  in  which  the  two  component  parts  are  independent  except 
at  one  point.  In  the  figure  one  winding  is  dotted,  the  other  in  full 
line,  and  they  meet  at  the  beginning  of  the  spiral  1  at  the  point  A. 
When  the  brushes  are  wide  enough  to  touch  two  sections  at  least,  it 
is  clear  that  the  arrangement  is  simply  another  form  of  Fig.  55,  but 
singly  re-entrant  because  it  has  an  odd  number  of  spirals. 

It  thus  appears  that  whether  a  ring  winding  is  simplex,  duplex, 
or  triplex  depends  simply  upon  the  pitch  chosen  with  respect  to  the 
number  of  spirals,  but  the  re-entrancy  is  dependent  upon  the  total 
number  of  spirals.  From  which  the  following  rule  may  be  developed : — 

In  a  ring  armature  the  G.G.F.  of  the  number  of  windings  and  the 
number  of  spirals  gives  the  re-entrancy. 

And  for  the  word  "  winding  "  we  need  the  definition — 

A  set  of  spirals  placed  upon  the  core  permanently  in  series  with 
one  another,  and  forming  one  complete  annular  helix,  whether  closing 
upon  itself  or  not. 

With  this  definition  the  series  of  the  spirals  marked  1  to  16  in 
Fig.  57  is  just  as  much  a  winding  as  the  series  dotted  in  Fig.  55, 
although  in  the  former  case  the  particular  set  of  spirals  does  not 
close  upon  itself. 

Notation  to  express  these  Windings. — Just  as  a  winding 
made  up  of  two  or  more  independent  windings  is  denoted  by  an 
equivalent  number  of  independent  circles,  so  one  that  is  double  but 
singly  re-entrant  is  denoted  by  a  figure  made  up  of  two  circles  joined 
with  a  loop.  The  notation,  therefore,  expresses  exactly  the  form  in 
which  the  winding  would  appear  if  it  could  be  removed  from  the 
core  without  cutting.  Thus — 

Simplex  singly  re-entrant  is  denoted  by  o 

Duplex  doubly  „  o  o 

Triplex  triply  „  o  o  o 

Duplex  singly  „  GD 

Triplex  singly  „  <£A> 

Sextuplex  triply  „  GD  GD   GD 

Quadruplex  doubly  „  GD  GD 
and  so  on. 

Quadruple  Winding  Doubly  Re-entrant. — Now,  in  Fig.  57 
we  might  (if  there  were  room  in  the  diagram)  insert  another  winding 
exactly  like  that  already  drawn,  with  the  spirals  of  the  new  winding 
occurring  alternately  with  those  of  the  old.  This  would  give  62 
spirals  upon  the  armature  (in  place  of  31),  a  distance  pitch  of  ^ 
(instead  of  ^-) ;  and  on  the  armature  there  would  be  two  windings, 
each  double,  and  each  independent  of  the  other.  This  additional 
winding  would  again  double  the  number  of  commutator  sections,  and 


102    'CONTINUOUS   CURRENT  MACHINE   DESIGN 

if  the  brush  were  wide  enough,  would  simply  be  placed  in  parallel 
with  the  original  winding.  This  arrangement  would  be  described  as 
a  quadruple  multiple-circuit  ring  winding  doubly  re-entrant,  and  it 
would  be  denoted  by  ©  Co)  as  explained  above. 

From  these  ring  windings  the  corresponding  drum  windings,  as 
described  below,  may  easily  be  developed. 


FIG.  58. — DUPLEX  SINGLY  KE-ENTRANT  DRUM  WINDING. 

The  Duplex  Drum  Singly  Re-entrant. — The  characteristic 
feature  of  the  double  or  duplex  drum  winding  was  (see  p.  99)  the 
difference  y/  —  y&  ==  ±4,  and  the  winding  was  doubly  re-entrant 
provided  the  total  number  of  conductors  was  a  multiple  of  4,  or  the 
total  number  of  coils  (of  one  turn  each)  was  divisible  by  2  (i.e.  by  the 
number  of  windings).  If  we  take  a  drum  to  correspond  with  the  ring 
of  Fig.  57,  there  will  be  upon  it  62  conductors  (or  31  coils),  and 
since  the  pitch  is  to  be  that  of  a  double  winding,  we  have — 

Pole  pitch  =  5/  =  15J 

y/  =  Sa7  13 
yf  -  ?/6  =  ±4 

yb  =  17  (retrogressive) 


ARMATURE  WINDINGS  103 

Thus  the  winding  table  is — 

1—18—5—22—9,  etc. 

But  the  winding  is  no  longer  doubly  re-entrant,  because  31  is  no  longer 
divisible  by  m  =  2.  The  winding,  as  a  matter  of  fact,  re-enters  itself 
after  taking  in  all  the  conductors,  thereby  becoming  singly  re-entrant, 
exactly  as  is  the  case  with  the  ring  armature  of  Fig.  55.  Following 
out  the  table,  after  the  fifteenth  lap,  conductor  61  is  reached,  and  we 
pass  to  No.  3  according  to  the  table — 

61— 16~3_20~~7,  etc. 

so  that  the  winding  naturally  closes  after  fifteen  more  laps. 

If  each  of  the  brushes  covers,  as  before,  at  least  2  segments,  the 
winding 

1— 18—5—22— 9,  etc. 

is  placed  in  parallel  with  the  winding 

3_20~~7_24—11,  etc. 

The  number  of  armature  circuits  is,  of  course,  the  same  as  in  the 
duplex  doubly  re-entrant  winding,  and  the  commutator  pitch  is  like- 
wise 2. 

As  far  as  commutation  and  current  capacity  of  the  armature  are 
concerned,  there  is  no  difference  between  the  two  kinds  of  duplex 
windings.  The  question  as  to  which  would  be  used  depends  on  the 
number  of  coils  it  is  possible  to  place  on  the  armature,  whether  even 
or  odd. 

Re-entrancy  of  Lap  Windings.— It  will  be  noted  that  the 
G.C.F.  of  the  number  of  coils  (32)  and  the  number  of  windings  (2) 
in  the  doubly  re-entrant  winding  is  2,  but  that  for  the  duplex  singly 
re-entrant  from  it  is  1.  Whence  we  get  a  rule  which,  extended  for 
multiplex  lap  windings,  is  stated  thus — 

The  re-entrancy  of  multiple-circuit  windings  is  the  G.C.F.  of  the 
number  of  windings  and  of  the  number  of  coils. 

From  the  considerations  here  outlined,  a  series  of  rules  governing 
multiple-circuit  or  lap-windings  can  be  drawn  up. 

Such  a  series  is  appended  below,  and  refers  to  armatures  with  one 
turn  per  commutator  section.  For  coil- wound  armatures  see  p.  110. 

Summary  of  Rules  for  Multiple-circuit  Drum  "Windings. — 
1.  Multiple-circuit  drum  windings  are  necessarily  lap  windings,  and 
follow  the  same  general  rules  as  ordinary  ring  windings,  being  sim- 
plex, duplex,  triplex,  etc.,  according  to  the  number  of  pairs  of  parallel 
paths  per  pole  in  the  armature. 

2.  A  duplex  or  multiplex  winding  may  be  singly  or  multi-re- 
entrant, but  this  re-entrancy  depends  entirely  upon  the  number  of 
surface  conductors, 

3.  There  must  be  in  all  cases  an  even  number  of  conductors,  which 


104     CONTINUOUS   CURRENT   MACHINE   DESIGN 

must  be  a  multiple  of  the  number  of  commutator  sections,  and  in  the 
case  of  slotted  armatures  a  multiple  of  the  number  of  slots. 

4.  The  number-pitches  for  any  single  re-entrant  winding  must  be 
odd  and  consequently  for  each  independent  winding  or  set  of  wind- 
ings the  number-pitches  considered  ivithout  reference  to  other  windings 
upon  the  same  armature  must  be  odd.     From  this  it  follows  that  for 
a  double-wound  doubly  re-entrant  armature  the  number-pitches  may 
be  both  even  numbers ;  but  generally  odd  numbers  are  taken. 

5.  The  number-pitches  for  any  number  of  conductors  must  differ 
by  a  number  =  2m,  where  m  is  the  number  of  windings. 

6.  The  re-entrancy  is  =  G.C.F.  of  w/2  and  m,  where  w  is  the  num- 
ber of  conductors. 

7.  The  forward  number-pitch  will  usually  be  approximately  equal 
to  w/p,  where  p  is  the  number  of  poles. 

8.  The  number  of  sets  of  brushes  is  equal  to  the  number  of  poles, 
and  each  brush  must  cover  a  number  of  segments  on  the  commutator 
greater  than  m  —  1. 

Equalizing  Rings. — In  multiple-circuit  windings,  it  is  essential 
that  the  E.M.F.'s  in  the  armature  sections  be  exactly  equal,  otherwise 
cross-currents  will  flow  between  them  which  increase  the  heating  of  the 
armature  and  thereby  limit  the  capacity  of  the  machine  for  a  definite 
temperature  rise.  Since  the  number  of  conductors  per  section  is 
equal,  such  difference  in  the  E.M.F.'s  of  the  sections  can  only  depend 
on  differences  in  the  flux  per  pole.  But  it  is  conceivable  with  lap 
windings  that  differences  in  the  depth  of  air-gap  (as,  for  instance,  when 
the  babbit  of  the  bearings  wears  away  and  the  armature  is  out  of 
centre)  and  differences  in  the  reluctance  of  the  various  magnetic 
circuits  might  cause  the  flux  to  be  unsymmetrically  distributed 
between  the  poles.  To  prevent  them  from  passing  through  all  the 
armature-bars,  these  cross-currents  are  allowed  to  circulate  through 
what  are  termed  equalizing  rings,  whereby  the  potentials  of  the 
sections  are  levelled. 

Suppose,  for  example,  an  armature  with  144  conductors  intended 
for  an  8-pole  machine.  The  number  of  conductors  per  pole  =  18, 
and  hence  the  number  pitch  between  conductor  1  and  the  conductor 
similarly  situated  at  an  adjacent  similar  pole  =  36.  Hence  con- 
ductors 1,  37,  73,  and  109  occupy  the  same  positions  with  respect  to 
their  north  poles,  and  should  therefore  have  the  same  potential  if  the 
fluxes  cut  were  the  same.  In  order  to  level  their  potentials,  they  are 
connected  to  ring  No.  1.  If  other  conductors  are  to  be  connected  in 
the  same  way,  we  may  fix  on  9  equalizing  rings.  Then  for  the  36 
conductors  for  each  pair  of  poles  we  must  space  the  connections  to 
the  equalizing  rings  every  fourth  conductor.  Thus  5,  41,  77,  113  are 
connected  to  the  next  ring,  and  9,  45,  81,  117  to  the  third,  and  so  on. 
The  more  equalising  rings  used  the  less  are  the  cross-currents  in  the 


FIG.  59. — INTERPOLE  MACHINE  SHOWING  EQUALIZER  RINGS 
(PHCENIX  DYNAMO  COMPANY). 


r 


FIG.  71.— WAVE-WOUND  ARMATURE. 


[To  face  p.  104. 


ARMATURE   WINDINGS 


105 


armature  bars.  The  cross-currents  are  confined  mostly  to  ,the  equal- 
izing rings  and  their  connections,  and  tend  by  armature  re-action  to 
diminish  the  differences  in  the  fluxes  cut  by  the  armature  sections. 
The  equalizing  rings  are  connected  either  to  the  segments  of  the 
commutator  which  are  joined  to  the  conductors  mentioned  above, 
or  else  the  rings  are  connected  at  the  rear  end  of  the  armature  to  the 
rear-end  connections  as  in  copper  strap- wound  armatures.  Fig.  59 
shows  a  modern  machine  with  equalizing  connections  to  its  armature. 
Two-circuit  or  Wave  Windings. — In  the  multiple-circuit 
winding  on  p.  95,  after  proceeding  with  the  odd  front  pitch  to  the 


FIG.  60. — SIMPLE  WAVE  WINDING. 


adjacent  pole,  the  winding  returned  to  the  next  old  conductor  under 
the  pole  from  which  it  started  as  shown  by  the  thickened  type  in  the 
winding  table — 


1  . 


Even     —    o  Even 

number  number 

Old  New  Old  New 

conductor     conductor 


5 

Old 


If  instead  of  returning  to  the  next  old  conductor  3,  which  lies 
under  the  same  north  pole  as  1,  we  proceed  to  an  old  conductor 
occupying  a  corresponding  position  under  the  next  north  pole,  and 
thence  to  a  "  new  "  conductor  under  the  next  south  pole  and  so  on,  we 
have  the  characteristic  feature  of  the  wave  or  two- circuit  winding. 


io6     CONTINUOUS   CURRENT   MACHINE   DESIGN 

Fig.  60  is  a  diagram  of  a  four-pole  machine  with  18  conductors 
on  the  armature.  If  a  constant  forward  pitch  of  5,  were  chosen,  the 
scheme  of  winding  would  be — 


Note  that  after  visiting  all  the  poles,  namely,  after  the  pth  connection 
(p  =  4  in  this  case),  we  arrive  at  3,  the  adjacent  old  conductor. 
Compare  this  with  a  lap  winding,  where  after  the  second  connection 
we  arrive  at  this  adjacent  (old)  conductor.  In  the  two-circuit  or 
wave  winding,  after  another  p  ( =  4)  connections  the  winding  reaches  5, 
and  so  on ;  hence  the  winding  progresses  by  what  is  termed  a  creep 
of  2. 

Circuits  and  Brushes  in  Two-circuit  Windings. — In  Fig.  61 
we  have  the  development  of  Fig.  60 ;  Fig.  62  is  a  second  develop- 


2         3         4         ft         «         T         8         •        10        II       13        13       M       IS        16       17       18 


6       U        16       3         6          13       II         ft      10        15          27         12        17       «         9          14 

yyyytiuuy 

3    d=3    C=D    crp   C±D   C±D   r~IL~>    CZ^D    r~^ 


AS  CO 

FIG.  62. 


rnent,  giving  the  order  of  the  conductors  as  they  are  connected 
(instead  of  the  order  of  position).  The  electromotive  forces  induced 
under  the  respective  poles  are  indicated  by  the  direction  of  the 
arrows.  Obviously  brushes  must  be  placed  for  collection,  wherever 
in  the  winding  two  series  of  E.M.F.'s  are  in  opposition.  This  is  seen 
to  be  the  case  at  C  and  at  A.  Two  brushes  at  C  and  A  divide 
the  armature  into  two  circuits  only,  whence  the  name.  Starting  with 
the  positive  brush,  and  following  through  the  winding  clockwise  till 


ARMATURE   WINDINGS  107 

we  reach  the  negative  brush,  it  will  be  noted  that  one  half  the  con- 
ductors on  the  armature  have  been  passed  over.  The  same  procedure 
counter-clockwise  will  take  in  the  other  half  of  the  conductors. 

It  is  also  clear  from  Fig.  62  that  we  might  have  obtained  the 
same  result  by  placing  the  brushes  at  B  and  D  respectively  instead 
of  at  A  and  C. 

Now,  from  Fig.  61  it  is  seen  that  the  segments  A  and  C  are  90° 
apart,  and  so  also  are  the  segments  B  and  D.  Either  pair  then  may 
be  used,  and  there  is  no  reason  why  both  should  not  be  made  use  of  ; 
for  the  conductors  lying  between  the  two  positive  brushes  C  and  D 
are  inactive,  and  so  also  are  those  connected  in  series  between  the  two 
negative  brushes  A  and  B.  The  addition  of  the  two  brushes  B  and  D, 
then,  practically  amounts  to  an  increase  of  the  size  of  the  brushes 
A  and  C,  and  affords  an  easy  means  of  increasing  the  area  of  brush- 
contact  without  increasing  the  length  of  the  commutator.  For 
machines  having  p  poles,  a  two-circuit  winding  would  require 
positive  and  negative  brushes  on  commutator  segments  spaced 
approximately  360  /p  degrees  apart,  and  the  number  of  paths  through 
the  armature  winding  is  entirely  independent  both  of  the  number 
of  brushes  and  of  the  number  of  poles.  This  should  be  contrasted 
with  the  multiple-circuit  winding,  in  which  the  number  of  paths 
through  the  armature  is  equal  to  the  number  of  poles  ;  whence 
the  multiple-circuit  armatures  are  sometimes  termed  parallel  wound, 
as  distinguished  from  two-circuit  armatures,  which  are  said  to  be 
series  wound. 

In  conformity  with  the  notation  for  the  multiple-circuit  armature 
on  p.  95,  the  paths  through  this  two-  circuit  winding  with  two 
brushes  may  be  expressed  thus  :  — 

/7,  2,   15,  10,  5,  18,  13,  8y 

+  brush  C  \  >  —  brush  A 

\12,  17,  4,  9,  14,  1,  6,  11,  16,  3/ 

Resistance  of  a  Two-circuit  Winding.  —  This  is  easily  seen 
to  be  given  by  the  expression 


in  which  p  =  specific  resistance  of  copper  at  the  specified  temperature 
/'  =  total  length  of  wire  in  the  armature  winding, 
a  =  sectional  area  of  the  wire.  i 

Formula  for  Two-circuit  Winding.  —  The  number  of  con- 
ductors of  a  two-circuit  winding  must  be  even.  This  is  easily  seen  to 
be  true,  since  the  last  connection  must,  after  regular  front  and  back 
pitches,  naturally  join  to  that  end  of  the  first  conductor  which  is  open. 
Evidently  the  number  of  end-connections  (both  forward  and  back) 
must  equal  the  number  of  conductors,  and  must  be  even.  The  front 


io8    CONTINUOUS   CURRENT   MACHINE   DESIGN 

and  back  pitches  (viz.  end  connections)  are,  wherever  possible,  taken 
the  same,  and  must  be  odd,  otherwise  only  half  the  conductors  would 
be  included. 

Thus  yf=yb  =  y  (say) 

If  y  be  made  equal  to  the  pole- pitch,  then  after  p  connections 
the  winding  closes,  and  only  p  conductors  have  been  connected  in  ;  so 
that  for  any  large  number  of  conductors  we  must  take  such  a  pitch  as 
shall  gradually  include  all  the  armature  conductors.  The  pitch  which 
fulfils  this  condition  and  is  nearest  to  the  pole  pitch  is  given  by  the 
equation — 

y  =  (conductors  ±  2)  poles  ;  i.e. 
y  =  (w  ±  2)p 

Creep. — The  difference  py  —  iv  =  2  constitutes  the  creep  of  the 
winding  after  p  connections  with  a  regular  pitch  of  y.  Starting  at 
conductor  1  in  any  winding,  after  p  connections  we  shall  arrive  at 
conductor  3,  and  after  another  p  connections  at  5,  and  so  on  till  all 
the  odd  conductors  are  included.  The  even  conductors  must  neces- 
sarily be  also  included,  because  the  pitch  is  odd.  On  p.  105  we 
have  a  four-pole  case  with  18  conductors — 

4#  -  18  =  2 
hence  y  =  5 

Progressive  and  Retrogressive  Wave  Winding. — The  formula 

w  =  py  -  2 
will  give  a  progressive  wave  winding,  and 

^  =  py  +  2 

a  retrogressive  wave  winding. 

Forward  and  Back  Pitches. — In  the  general  formula 

w  —  py  ±  2 

it  has  been  said  that  y  must  be  an  odd  number.  If  for  given  values 
of  w  and  p,  y  comes  out  an  even  number,  then  odd  forward  and  back 
pitches  must  be  chosen. 

Thus  for  w  =  22  and_p  =  4 

22  =  4y  —  2  (progressive) 
y  =  6 

Hence  ?//  =  7  and  y&  =  5  are  chosen,  y  being  the  mean  of  yf  and  yb. 

In  general,  provided  they  are  odd  and  give  the  correct  mean  pitch, 
any  pair  of  pitches  may  be  used ;  and  this  is  sometimes  important  to 
remember  when  a  number  of  slots  happens  to  be  adopted  which  does 
not  work  in  well  with  the  best  pair  of  pitches.  Thus  in  the  above 
case,  if  it  were  more  convenient,  yf  =  9,  yb  =  3  might  have  been 
adopted,  for  the  creep  would  have  been  the  same;  and  for  wave 


ARMATURE   WINDINGS  109 

windings  the  difference  between  the  number-pitches  does  not  decide 
whether  the  winding  is  simplex  or  multiplex,  as  it  does  for  lap 
windings. 

Commutator  Pitch  of  Two-circuit  Windings. — The  com- 
mutator pitch  is  equal  to  the  mean  pitch,  and  in  the  above  example 
is  6 ;  for  the  commutator  connections  take  place  at  every  backward 
pitch,  and  the  pitch  from  one  backward  connection  to  the  next 
backward  connection  is  equal  to  yj  4-  yb.  The  number  of  commutator 
segments  is,  however,  half  the  number  of  conductors ;  hence  the 

commutator  pitch  is  -f  0      ,  i.e.  the  mean  pitch  y. 

A 

Multiplex  Wave  Windings. — In  Fig.  60  we  could  place  on 
the  armature  another  two-circuit  winding  as  indicated  by  the  dotted 
lines  in  the  diagram.  This  second  winding  would  be  exactly  similar 
to  the  first,  and  would  have  its  commutator  sections  interleaved  with 
those  of  the  other.  Such  an  arrangement  would  constitute  a  duplex 
wave  winding  doubly  re-entrant.  The  formula  for  such  a  winding 
can  easily  be  shown  to  be 

w  =  py  ±  4 

but  y  is  now  even,  for  y  will  be  equal  to  2yr,  where  y'  is  the  pitch  for 
each  winding  considered  separately. 

For  a  duplex  singly  re-entrant  wave  winding,  the  formula  is  again 
the  same,  w  =  py  ±  4,  but  y  becomes  odd. 

The  general  equation,  then,  for  multiplex  wave  windings  is 
w  =  py  ±  2m,  where  ra  =  number  of  windings,  and  the  general  rules 
governing  wave  windings  of  one  turn  are  collected  together  below. 
Coil  windings  are  considered  on  p.  110. 

Importance  of  Multiplex  Two-circuit  Drum  Windings. — 
As  the  two-circuit  simplex  winding  has  only  two  circuits,  the  voltage 
developed  is  higher  than  that  of  the  corresponding  multiple-circuit 
case  where  there  are  more  than  two  poles.  Hence,  if  the  current  to 
be  collected  is  too  heavy  for  a  two-circuit  winding,  it  is  usual  to 
adopt  the  multiple-circuit  type.  Thus  the  multiplex  forms  of  the 
two-circuit  winding  are  relatively  unimportant,  and  the  multiplex 
forms  of  multiple-circuit  windings  are  only  necessary  for  such 
purposes  as  plating  or  for  electric  furnaces. 

Rules  governing  Two-circuit  Windings. — 1.  Two-circuit 
windings  are  of  necessity  "  wave  "  windings,  the  system  of  end  con- 
nections being  such  as  to  pass  continually  in  one  direction  around  the 
armature  periphery  when  the  winding  is  reduced  to  its  simplest 
form — i.e.  with  one  turn  per  commutator  section. 

2.  These  armatures  may  be  simplex,  duplex,  triplex,  etc.,  accord- 
ing to  the  number  of  parallel  paths  (through  the  armature)  from 
brush  to  brush. 

3.  A  multiplex  winding  may  be  singly  or  multi-re-entrant ;  this 


i  io    CONTINUOUS   CURRENT   MACHINE   DESIGN 


re-en  trancy  depending  upon  the  relationship  between  the  pitch  and 
the  number  of  windings. 

4.  There  must  be  in  all  cases  an  even  number  of  conductors, 
which  must  be  a  multiple  of  the  number  of  commutator  sections 
(and  also,  in  the  case  of  a  slotted  armature,  of  the  number  of  slots). 

5.  The  rules  for  connection  are  given  by  the  general  formula 

w  =  py  ±  2m 

where  w  is  the  number  of  conductors ; 
p  is  the  number  of  poles ; 
m  is  the  number  of  windings  required ; 
y  is  the  mean  pitch. 

y  must  for  all  simplex  windings  be  either  an  odd  number,  or  two 
odd  number-pitches  must  be  used  alternately  as  (y  +  1)  and  (y  —  1). 

For  multiplex  windings,  y  should  be  either  an  odd  number  or 
"  m  "  times  an  odd  number,  or  some  multiple  less  than  m  of  an  odd 
number.  Attention  to  this  will  obviate  the  use  of  different  pitches 
at  the  two  ends  of  the  armature. 

The  re-entrancy  is  given  by  the  G.C.F.  of  m  and  y. 

The  number  of  sets  of  brushes  absolutely  essential  is  two,  one 
positive  and  one  negative.  But  there  may  be  more  sets  in  parallel 
with  these  according  to  the  number  of  poles.  Each  brush  must  cover 
a  number  of  segments  on  the  commutator  greater  than  m  —  1. 

Coil  and  Slot  Windings. — All  the  armatures  so  far  discussed, 
with  the  exception  of  Fig.  51,  have  been  shown  with  but  one  turn 
per  commutator  section.  This  arrangement  is  only  met  with  in 
large  generators  or  motors ;  in  smaller  machines  more  than  one  turn 
per  section  is  common,  and  the  winding  diagrams  must  be  adapted 
to  fit  this  case.  Moreover,  all  modern  armature  cores,  large  and 
small,  are  slotted  so  that  the  winding  may  be  better  fixed  and  driven. 


FIG.  63. — CONNECTION  OF  LAP- 
WOUND  ABMATUEE  COIL. 


FIG.  64. — TWO-CIRCUIT 
ABMATUBE  COIL. 


Coil  Windings.— Now  with  reference  to  the  first  matter,  i.e. 
the  substitution  of  coils  for  single  turns,  consider  one  turn  or  element 


ARMATURE   WINDINGS  in 

of  the  development,  Fig.  54.  This  is  made  up  of  two  conductors,  a  back 
connection,  and  two  leads  to  the  commutator.  Now  substitute  for 
this  element  the  coil  shown  in  Fig.  63,  and  it  will  be  seen  that  the 
surface  conductors  become  "  coil-sides,"  and  the  connections  to  the 
commutator  are  the  ends  of  the  coil.  Thus  the  pitch  at  the  end 
remote  from  the  commutator  is  settled  by  the  coil  shape  and  size, 
whilst  that  at  the  commutator  end  is  settled  by  the  connections  to 
the  commutator. 

In  an  exactly  similar  way  for  two-circuit  windings,  one  element 
or  turn  of  the  larger  armature  may  in  a  smaller  machine  be  replaced 
by  one  coil,  as  in  Fig.  64,  and  here  again  the  coil  shape  settles  one 
pitch,  the  commutator  connection  the  other. 

Grouping  of  Conductors  in  Slots. — When  slots  are  used,  the 
surface  conductors  are  naturally  not  dis- 
tributed   uniformly    over    the    armature 
surface,   but   are   grouped   in   the  slots. 
So  long  as  there  is  only  one  armature 
turn  per  commutator  section,  no  trouble 
should  be  occasioned  by  the  arrangement 
of  the  conductors  in  these  groups,  pro- 
vided  that  the   numbering  of  the   con- 
doctors  be  carried  out   as  suggested  in     Fl°'  "^JS?  ™ 
Fig.   65,   i.e.    all  even  numbers   be   ar- 
ranged at  the  top  of  the  slots,  all  odd  numbers  at  the  bottom  of 
the  slots. 

Fig.  66  illustrates  well  the  method  of  counting  surface  conductors 
and  pitches.  It  is  a  lap-wound  4-pole  drum  having  48  conductors 
and  24  slots. 

yf  =  15,  yb  =  13,  so  it  is  progressive  and  simplex,  with  a  commu- 
tator pitch  =  1. 

In  the  same  way,  Fig.  67  illustrates  a  two-circuit  six-pole  arma- 
ture with  64  conductors,  and  in  the  equation 

w  =  py  ±  2 
y=H 
The  slots  here  number  32,  and  the  commutator  pitch  is  11. 

Meaning  of  Slot  Winding-pitch. — When  the  coils  or  turns 
are  grouped  in  slots  in  this  manner,  it  is  easiest  for  the  winder, 
having  numbered  the  slots  consecutively,  to  reckon  from  the  slot 
winding-pitch  of  the  winding — i.e.  the  difference  between  the  numbers 
given  to  the  slots  in  which  the  two  sides  of  a  coil  lie.  If  we  be  given 
this,  and  the  commutator-pitch,  and  if  all  the  turns  be  placed  on  the 
armature  so  that  one  side  of  each  turn  is  at  the  top  of  a  slot  and  the 
other  side  at  the  bottom  (as  in  Figs.  66  and  67),  the  connection  to 
the  commutator  is  very  easy  and  the  result  quite  symmetrical.  The 
slot  winding-pitch  is  best  reckoned  at  the  end  remote  from  the 


ii2     CONTINUOUS   CURRENT   MACHINE   DESIGN 

6 

commutator,  i.e.  in  Fig.  66  it  is  7,  and  in  Fig.  67  it  is  *.     In  general 

it  is  -  (yf  Jt:  1),  where  c  is  the  number  of  surface  conductors  grouped 
in  one  slot. 


FIG.  66. — LAP- WOUND  FOUR-POLE  DRUM. 


In  Fig.  66  again  the  commutator  pitch  is  1,  and  in  Fig.  67  it  is 

— J —  =11.     Given  these  instructions,  it  is  easy  for  the  winder  to 

2 

proceed  by  taking  care  that  each  turn  spans  a  number  of  teeth  equal 
to  the  slot  winding-pitch,  and  that  the  commutator  ends  of  these 
coils  have  the  right  commutator-pitch. 

Grouping  of  Coils  in  Slots. — By  following  out  the  substitution 


ARMATURE   WINDINGS 

of  coils  for  turns  exactly  as  on  p.  Ill,  the  meaning  of  the  "  slot 
winding-pitch"  and  "commutator-pitch"  for  such  cases  becomes 
apparent.  The  coil  sides  take  the  place  of  conductors  in  the  slots, 
so  that  the  coil  itself  must  be  made  to  span  a  number  of  teeth  equal 
to  the  slot  winding-pitch.  The  ends  of  the  coil  are  brought  down  to 
the  commutator,  and  there  fixed  to  the  segments  with  the  correct 


FIG.  67. — WAVE- WOUND  SIX-POLE  DRUM. 

commutator  pitch.  For  multiple-circuit  winding  this  is  easy  enough, 
since  the  slot  winding-pitch  should  be  about  equal  to  the  pole-pitch, 
and  the  ends  of  the  first  coil,  for  simplex  windings,  must  come  to 
neighbouring  segments  (Fig.  63)  ;  while  for  the  second  coil  one  end 
will  go  to  the  right-hand  segment  of  Fig.  63,  say,  and  the  other  end 
will  go  to  the  next  commutator  segment  to  the  right  again,  and  so  on. 
As  an  example,  suppose  an  armature  for  a  4-pole  machine  having 
47  slots,  94  coils,  each  coil  consisting  of  4  turns.  The  commutator 
must  have  94  segments,  and  each  slot  must  hold  4  coil-sides.  The 

I 


ii4     CONTINUOUS   CURRENT   MACHINE   DESIGN 

slot  pitch  may  be  \7  =  say  11,  so  that  the  first  coil  lies  at  the  left- 
hand  side  of  slots  1  and  12.  The  ends  are  brought  down  to  segments 
1  and  2.  The  second  coil  lies  at  the  right-hand  side  of  slots  1  and 
12,  and  its  ends,  for  progressive  winding,  go  to  segments  2  and  3, 
and  so  on. 

In  such  a  case  if  we  count  coil-sides  as  surface  conductors,  we 
have — 

Total  number  of  coil-sides  188  of  four  conductors  each. 

yf  =  45 

For  wave  windings  the  case  is  not  quite  so  simple,  because  the 
arrangement  must  follow  a  rigid  formula.  The  best  way  to  proceed 
is  to  number  the  coil-sides  as  they  will  lie  in  their  slots  in  accordance 
with  Fig.  65.  Then  write  the  formula  w  =  py  ±  2  in  the  form, 
coils  =  (pole  pairs  X  y)  ±  1.  y  is  then  the  mean  pitch,  and  from  it 
yf  may  be  obtained  as  =»  y  if  this  be  an  odd  number,  or  =  y  ±  1,  if  y 
be  even ;  yb  being  similarly  =  y  or  y  +  1.  The  slot  pitch  is  then 
obtained  by  dividing  (y/—  1)  by  the  coil-sides  in  one  slot;  Thus, 
suppose  an  armature  having  41  slots,  three  coils  per  slot,  i.e.  six  coil- 
sides  in  each  slot,  as  in  Fig.  87.  If  the  field  have  4  poles  and  the 
winding  be  two-circuit,  we  get — 

Total  number  of  coils  =  123 

123  =  2y  ±  1 
whence  y  =•  62  or  61 

This  gives  a  choice  of  three  windings,  viz.  — 

(1)  yf  =  61,     yb  =  61 

(2)  yf  =  61,     yb  =  63 

(3)  yf  =  63,    yb  =  61 

Since  there  are  six  coil-sides  in  one  slot,  the  best 
value  of  yf  would  be  61,  for  (61  -  1)  is  divisible 
by  6. 

Thus  the  slot  winding-pitch  becomes  10,  the 
commutator-pitch  61.  The  diagram  for  the  whole 
winding  is  shown  more  clearly  in  Figs.  68  and  129, 
from  which  it  will  be  seen  that  each  set  of  three 
coils  is  bound  together  so  as  to  have  the  appearance 
of  only  one  coil,  although  of  course  the  ends  are 
brought  out  separately,  as  depicted  in  Fig.  68. 
These  examples  of  the  arrangement  of  coil  windings  in  slots 
should,  it  is  thought,  suffice.  Multiplex  forms  of  such  windings  are 
of  course  rarely  met  with ;  for  a  multiplex  winding  is  only  of  use  after 
the  winding  has  been  reduced  to  one  turn  per  segment  and  yet  fewer 
bars  in  series  are  required. 


ARMATURE  WINDINGS 


Idle  or  Dummy  Coils. — It  is  clear  that  though  for  lap  windings 
any  number  of  slots  may  be  adopted,  yet  for  wave  windings  the 
number  of  coils,  and  consequently  of  slots,  is  limited  by  the  formula 

Coils  =  (pole-pairs)  y  ±  1 

If  y  is  to  be  odd,  clearly  when  the  number  of  pole-pairs  is  odd  the 
number  of  coils  will  be  even,  and  vice  versa.  Since  the  number  of 
coils  should  be  a  multiple  of  the  number  of  slots,  the  number  of  slots 
appropriate  to  an  odd  number  of  pole-pairs  will  be  even,  and  vice  versa. 
But  it  sometimes  happens  that  a  standard  armature  is  .available, 
having  a  number  of  slots  not  according  with  the  above  statement. 
In  such  cases  one  or  more  coils  may  be  "  dummies/'  i.e.  not  connected 
to  the  commutator,  but  inserted  to  render  the  winding  balanced  and 
symmetrical. 

In  a  similar  way  idle  commutator-bars  are  sometimes  used  to 
make  use  of  a  standard  commutator. 

Best  Numbers  of  Slots  for  Two-circuit  Windings.— A  little 
consideration  shows  that  the  series  29,  33,  37,  41,  45,  49,  etc.,  is  best 
for  4-pole  machines  with  an  odd  number  of  coils  per  slot.  Similarly, 
for  6-pole  windings  the  series  26,  32,  38,  etc.,  with  two  coils  per  slot 
gives  good  regular  windings.  And  so  on,  for  each  number  of  poles 
there  is  for  wave  winding  a  preference  in  the  number  of  slots  to  be 
used,  so  that  when  armatures  may  be  required  for  either  lap  or  wave 
windings  the  standard  number  of  slots  is  usually  chosen  to  suit  the 
latter. 

Comparison  of  Lap  and  Wave  Windings.— 1.  Appearance. 
It  is  usually  possible,  with  bar- wound  armatures,  to  tell  the  style  of 
winding  from  the  appearance.  For  in  the  case  of  lap-windings  the 
bar,  as  it  lies  on  the  armature,  bends  in  the  same  direction  at  both 
ends  (Fig.  69),  while  in  the  case  of  wave  winding  it  bends  in  opposite 
directions,  as  is  clearly  seen  in  Figs.  70  and  71. 


FIG.  69. — APPEARANCE  OF  LAP- 
WINDING. 


FIG.  70. — APPEARANCE  OF  WAVE- 
WINDING. 


2.  Electrical  Balance.  It  has  been  pointed  out  on  p.  104  that  lack 
of  symmetry  of  the  magnetic  field  causes  parasitic  currents  in  lap 
windings,  and  that  equalizing  rings  are  used  to  obviate  these.  With 
wave  windings,  since  between  brush  and  brush  there  are  conductors 


ii6    CONTINUOUS   CURRENT   MACHINE   DESIGN 

in  series  under  all  the  poles,  such  an  effect  cannot  follow  from  a  lack 
of  field  symmetry,  and  equalizing  rings  are  consequently  unnecessary. 
On  the  other  hand,  with  wave  windings  having  an  even  number  of 
pole-pairs  an  odd  number  of  commutator  sections  is  often  a  necessity ; 
and  this  results  in  commutation  which  is  not  simultaneous  at  all  the 
brushes,  as  is  clearly  evident  from  Fig.  60.  Indeed,  with  all  wave 
windings  this  must  occur  more  or  less,  as  by  the  formula  the  number 
of  coils  can  never  be  an  exact  multiple  of  the  number  of  poles.  The 
result  of  this  and  of  the  system  of  connection  is,  that  what  is  termed 
"  selective  commutation "  occurs ;  that  is,  there  is  a  tendency  for 
the  current  to  be  collected  at  those  brushes  which  have  the  lower 
resistance.  Thus  the  author  has  known  of  cases  where  removing  two 
rows  (one  +  and  one—)  of  brushes  from  a  4-pole  wave- wound 
machine  has  distinctly  improved  commutation,  although  the  current- 
density  under  the  brushes  must  have  been  forced  up  very  much 
thereby. 

The  Same  Armature  as  Wave  Wound  and  Lap  Wound. — 
It  is  clear,  from  Figs.  63  and  64,  that  exactly  the  same  coils  may  in 
some  cases,  be  used  for  both  classes  of  winding,  the  connections  to  the 
commutator  only  being  changed.  Thus  a  4-pole  wave- wound  armature 
will  give,  in  a  certain  field,  at  a  certain  speed,  an  electromotive 
force  =  V,  and  will  carry  without  undue  heating  a  current  of  C 
amperes. 

If,  on  the  other  hand,  we  arrange  it  for  a  multiple-circuit  winding, 
the  coils  will  be  the  same,  but  the  connections  of  the  coils  to  the 
commutator  will  be  changed.  The  armature  will  then  give  E/2  volts, 
and  at  the  same  current  density  as  before  20  amperes,  with  the  same 
field  and  at  the  same  speed.  This  interchangeability  is  most  useful 
to  remember  where  many  outputs  are  required  from  standard  arma- 
tures ;  and  in  getting  out  new  patterns  of  armature  discs  it  should 
always  be  borne  in  mind  that,  while  any  even  number  of  surface 
conductors  may  be  used  for  a  simple  multiple-circuit  winding,  the 
same  is  not  true  for  two-circuit  armatures. 

It  is  well,  therefore,  in  designing  the  disc,  to  keep  in  view  the 
possibility  of  having  to  use  it  for  a  two-circuit  winding  (cf.  p.  192). 

Finally,  the  differences  between  multiple  and  two-circuit  armatures 
increase  with  the  number  of  poles.  Thus,  if  a  10-pole  machine  with 
a  given  number  of  surface  conductors  be  arranged  as  multiple-  and 
as  two-circuit  respectively,  in  the  latter  case  it  will  give  five  times 
the  voltage  and  one-fifth  of  the  current  that  it  did  in  the  former, 
with  the  same  number  of  lines  per  pole  and  at  the  same  speed. 


CHAPTER  IX 


COMMUTATION 

SOMETIMES  machines  suitable  for  a  certain  output  as  far  as  tempera- 
ture rise  is  concerned  cannot  be  run  at  this  output  because  of  violent 
sparking  at  the  commutator.  Thus  commutation  plays  a  very 
important  part  in  design. 

Consideration  of  Commutation  in  Ring  Armatures. — Con- 
sider a  conductor  such  as  (1),  Fig.  72.    As  (1)  moves  round  to  position 
(5)  it  passes  from  a  position  in  which  it  cuts 
maximum  flux  to  a  position  in  which  it  cuts 
no  flux. 


FIG.  72.— COMMUTATION  IN 
A  RING  ARMATURE. 


FIG.  73.— CURVES  OF  E.M.F.  AND  CURRENT 

PER   CONDUOTOR. 


Thus  plotting  the  E.M.F.  generated  in  (1)  for  the  various  positions 
(1)  to  (5),  we  obtain  a  line  like  that  shown  in  Fig.  73,  graph  (1),  the 
E.M.F.  falling  from  a  maximum  to  zero. 

Now  consider  conductor  (2).  The  E.M.F.  curve  will  be  exactly 
similar  to  that  of  (1),  but  will  precede  it  by  a  time  proportional  to  the 
distance  between  the  two  conductors. 


n8     CONTINUOUS   CURRENT   MACHINE   DESIGN 

The  armature  E.M.F.  thus  forms  a  polyphase  system,  the  number 
of  phases  being  equal  to  the  number  of  commutator  segments  ;  but 
though  the  E.M.F.'s  at  any  given  instant  in  turns  (1),  (2),  and  (3)  thus 
differ,  the  current  in  the  three  turns  is  the  same. 

Now,  it  is  to  be  noted  that  the  turns  at  (7)  and  (8)  in  the  figure 
are  short-circuited  under  the  brush,  so  that  the  current  will  fall  to 
zero  as  (1)  reaches  (7).  The  current  is  then  constant  from  positions 

(1)  to  (6),  and  falls  to  zero 
about  position  (7)  ;  it  rises  to 
its  normal  value  again  beyond 
position  (8). 

Thus  the  continual  falling 
away   and    re-establishment   of 
the  E.M.F.  cannot  be  taken  ad- 
vantage of  to  cause  the  current 
Time  to  change  in  a  similar  gradual 

manner;  and  it  is  the  effect  of 
collecting  the  current  at  a  par- 
ticular point  that  causes  the  diffi- 
culty in  commutation,  because 
the  current  in  each  turn  must 
fall  to  zero,  and  then  rise  to  its 
normal  value  in  the  opposite 
direction  (Fig.  74)  when  the 
FIG.  74.—  FALL  OF  CURRENT  IN  CONDUCTOR  coil  is  connected  to  a  segment 
UNDERGOING  COMMUTATION.  under  the  brush. 

From  the  number   of  coils 

undergoing  this  complete  change  per  second  is  derived  the  frequency 
of  commutation  ;  obviously  — 

(1)  The  greater  the  width  of  brush  the  more  time  is  there  to  effect 
the  change. 

(2)  The  greater  the  speed  the  less  is  this  time. 
Now  — 

rp.         „  brush  width  in  segments  (  =  a) 

Time  of  commutation  (  =  tc)  =  -  r-r  —  =  --  §-T—   —  -  —  —  - 

peripheral  comr.  speed  in  segs.  per  sec. 

A  complete  cycle  is  taken  to  be  twice  that  represented  between 
A  arid  B  (Fig.  74). 

Let  ~  =  complete  cycles  per  second. 

rp,  «  ,  .          peripheral  speed  , 

Then  ~  of  commutation  =  £     r     -  ryrur  (  =  ~«) 

2  (brush  width)  v 

Let  n  =  revs,  per  second  ; 
S  =  number  of  segments. 


Then  ,     = 


2  (brush  width)      2g 


COMMUTATION  119 

Commutation  in  Drum  Armatures. — Though  the  case  as 
hitherto  presented  refers  particularly  to  ring  armatures,  it  applies 
equally  well  to  those  that  are  drum-wound.  It  is  merely  necessary 
to  substitute  for  one  turn  of  the  ring  in  Fig.  72  one  turn  of  the  drum 
Fig.  52,  when  it  is  clear  that  we  have  a  case  analogous  in  all  respects 
to  that  of  the  ring.  The  only  difference  is  the  position  of  the  loop  or 
turn  considered,  which  for  the  present  is  immaterial. 

Methods  of  Commutation. — If  a  circuit  carrying  a  current  be 
suddenly  opened,  an  arc  or  spark  will  almost  invariably  appear  at  the 
moment  and  place  of  opening,  unless  the  circuit  be  very  nearly  non- 
inductive.  It  is  possible,  however,  to  reduce  the  current  to  zero  in  a 
circuit  either  (1)  by  introducing  an  appropriate  counter  E.M.F.,  or  (2) 
by  introducing  a  resistance  gradually  increasing  in  value  up  to  infinity. 

These  considerations  lead  to  two  methods  of  satisfactorily  accom- 
plishing commutation,  called  respectively — 

(1)  E.M.F.  commutation  and  (2)  Resistance  commutation. 

In  E.M.F.  commutation  the  current  in  the  coil  under  the  brush  is 
stopped  and  reversed  by  an  opposing  E.M.F.  set  up  in  the  coil,  as,  on 
leaving  the  brush,  it  conies  under 

the  influence   of    the  "leading"  . ^.Mfc "^ KesistanceB™*' 

pole-tip*  or  special  commutating 
pole. 

Resistance      commutation      is 
brought  about  as  follows :  Imagine 
the  commutator  segments  moving 
as  indicated  by  the  arrow,  Fig.  75.     FIG.  75.— KESISTANCE  COMMUTATION. 
If,  to  begin  with,  the  segment  6 

just  touches  the  tip  (1)  of  the  brush,  the  resistance  between  b  and 
the  brush  will  be  very  high,  so  that  most  of  the  current  collected  will 
flow  through  c.  Conductor  (5)  will  then  have  to  carry  nearly  all  the 
current  in  (4).  As  I  comes  further  under  (1)  the  resistance  decreases 
so  that  more  current  flows  through  5,  i.e.  the  current  through  (5)  is 
decreasing.  When  the  brush  becomes  symmetrically  placed  with 
regard  to  (4)  and  (5),  as  in  the  diagram,  practically  the  same  amount 
of  current  will  flow  through  &  as  through  c,  half  the  total  flowing 
through  each.  Thus  the  current  in  (5)  has  been  reduced  to  zero. 
Further  motion  increases  the  resistance  of  c,  so  that  some  of  the 
current  will  flow  through  (5)  in  the  reverse  direction  and  pass 
through  &.  Finally,  the  resistance  of  c  is  so  great  that  all  the  current 
flows  through  (5)  in  the  reverse  direction  to  the  original  current. 

Thus  the  current  has  been  caused  to  change  from  a  certain  value 
through  zero  down  to  the  same  value  in  the  opposite  direction.  So 

*  The  "  leading "  pole-tip  of  any  pair  of  poles  in  a  dynamo  is  that  pole-tip 
towards  which  the  coils  of  the  armature  are  moving  as  they  leave  the  brush,  i.e.  as 
marked  A  in  Fig.  76. 


120     CONTINUOUS   CURRENT   MACHINE   DESIGN 

when  the  break  between  the  brush  and  c  actually  occurs,  there  is 
very  little  current  flowing  from  it  to  the  brush,  and  therefore  no 
spark.  This  is  the  foundation  of  so-called  resistance  commutation. 

The  two  methods  may  be  combined  in  practice,  i.e.  we  have  a  third 
method  possible,  viz. — 

(3)  Mixed  E.M.F.  and  resistance  commutation. 

(1)  E.M.F.  Commutation. — For  E.M.F.  commutation  a  strong 
and  constant  field  must  exist  under  the  leading  pole-tip  of  a  dynamo 
(or  trailing  pole-tip  of  a  motor). 

Failing  this,  it  is  necessary  for  every  increase  in  load  to  move  the 
brushes  forward  until  the  coils  under  commutation  are  in  a  strong 
field,  or  to  use  special  devices  to  effect  commutation.  The  former 
must  be  avoided,  not  only  on  account  of  the  constant  attention  the 
machine  would  need,  but  also  because,  in  addition  to  good  commuta- 
tion, small  regulation  is  required,  and  this  means  small  movement  of 
the  brushes.  As  an  ideal  position  the  brushes  should  be  on  the  no-load 
neutral  line.  In  the  case  of  reversible  motors,  such  as  tramway  and 
railway  motors,  it  is  essential  that  the  brushes  should  be  on  this  line. 

Of  special  devices,  very  many  have  been  proposed,  but  only  a 
few  of  these  are  satisfactory ;  the  best  are  given  below. 

(1)  Special  Commutation  Coils  on  the  Armature. — These  consist 
of  a  few  turns  of  wire   inserted   on  the  armature  in  between  the 
segment  and  main  winding,  and  spaced  so  that  when  a  segment 
is  under  the  brush  the  commutating  turns  connected  to  it  will  be 

under  the  leading  pole,  and  so  in 
a  strong  field.  This  produces  the 
necessary  reversing  E.M.F.  The 
brushes  may  then  be  arranged  for 
any  position  on  the  commutator. 
This  system  is  known  as  Sayers 
winding  (Fig.  76). 

A  Sayers  winding  is  satisfactory 

FIG.  76.— SAYERS  WINDING.  for  small  machines,  but  it  is  ex- 

tremely sensitive,  and,  for  some 

unknown  reason,  fails  for  machines  above  about  20  K.W.  The 
principle  itself  is  sound,  as  may  be  seen  on  small  machines,  where 
it  is  possible  to  obtain  sparkless  running  even  with  a  backward  lead 
(for  dynamos).  The  principle  may  be  carried  so  far  that  the  machine 
will  run  under  the  armature  field  alone,  the  main  field  coils  bein 
disconnected.  The  winding  is,  however,  rather  costly. 

(2)  Special  Shapes  of  Pole-tips. — The  steady  field  under  the  pole-tip 
may  be  obtained  by  means  of  saturation  in  the  pole-tips,  for  which 
various  devices  have  been  suggested.    One  method  consists  in  cutting 
slots  in  the  poles  near  to  the  leading  pole-tip,  and  another  plan  is  to 
specially  shape  the  shoe  so  as  to  make  it  very  narrow  at  the  saturated  tip. 


COMMUTATION 


121 


(3)  Specially    Wound  Tips  may  be  used,  the  coil  being   placed 
in  series  with  the  armature  (Fig.  77) ;  from  (3)  has  been  deduced — 

(4)  Special  Commutating  Poles. — In  this  case,  instead  of  wind- 
ing the  tip  of   the   pole,  the  main  pole  is  left  unchanged,  and    a 
small  pole   introduced   which   carries   the   coil   for   producing  the 
reversing  field  (Figs.  78  and  59). 

(5)  Ryan   Winding. — Instead  of  having  a  separately  wound  coil 
to  saturate  the  pole-tip  and  so  decrease  the  effect  of  the  cross  ampere- 
turns,  the  latter   may  be   neutralized   by  turns  passing  round  the 
armature  and  through  the  poles  (Fig.  79).     For  D.C.  machines  this 
winding  has  not  been  adopted  except  in  cases  of  very  high  speed, 


FIGS.  77,  78,  AND  79. — AIDS  TO  COMMUTATION. 

because  of  the  large  amount  of  copper  required,  which  may  amount 
to  more  than  that  necessary  for  the  armature. 

Usual  Methods. — Of  all  the  methods  for  improving  E.M.F. 
commutation  by  special  windings,  only  two  are  of  any  use  in  practice, 
namely,  (1)  the  commutating  pole  or  interpole,  and  (2)  the  Eyan 
winding;  and  since  the  latter  is  expensive,  we  are  only  left,  for 
ordinary  purposes,  with  the  commutating  pole. 

Calculation  of  E.M.F.  Commutation. — It  can  be  shown  that 
for  perfect  commutation,  the  commutating  E.M.F.  to  be  introduced 
into  the  coil  is  given  by  the  expression  *— 


e  =  Cwr 


1.4-i' 


l  --t  w 

See  Appendix  V.  and  paragraph  on  effect  of  self-induction,  infra. 


122     CONTINUOUS   CURRENT   MACHINE   DESIGN 

where  r  =  resistance  of  the  circuit  of  the  coil  under  commutation ; 
Lc  =  coefficient  of  self-induction  of  the  coil ; 
tc  =  time  of  commutation  ; 
Cw  =  the  current  per  conductor  in  the  armature. 
Of  these  quantities  Cw  is  known,  and  tc  is  easily  calculated  as 
shown  on  p.  118.     The  value  to  be  taken  for  r  is  dependent  upon 
many  considerations  ;  but  with  proper  E.M.F.  commutation  it  should 
be  possible  to  use  very  low  resistance  brushes.     In  this  case,  then, 
the  safest  course  is  to  regard  r  as  simply  the  resistance  of  the  coil. 
Calculation  of  Lc. — We  have  for  any  coil — 

j    __  (flux  set  up  in  1  turn  by  1  amp,  flowing  therein)  x  turns  X  turns 

c  "  108 

T2f 
i.e.  Lc  =  — ^,  where  T  =  No.  of  turns  per  coil,  and  /  =  field  set  up  by 

1  amp.  in  1  turn. 

Value  of  "  f "  by  Hobart's  Method.* — The  average  field  set  up 
by  1  amp.  turn  was  tested  for  various  slots,  and  the  following  con- 
clusion was  arrived  at : — 

For  a  ratio  of  slot-width  to  slot-depth  not  exceeding  3 '5,  the  flux  set 
up  is  on  the  average  10  C.G.S.  lines  per  inch  of  slot  (axial  length),  and 

2  C.G.S.  lines  per  inch  length  of  conductor  not  lying  in  the  slot  (for 
ordinary  drum  armatures). 

Now,  for  ordinary  drum  armatures,  the  length  of  mean  turn  on 
the  armature  =  L.M.T.a  =  2  x  net  iron  length  +  3  x  pole-pitch. 
.*.  C.G.S.  lines  per  amp.  turn  =  20  net  length  -f-  6  pole-pitch.  Now, 
for  all  D.C.  armatures  there  are  2  coil  sides  per  slot  simultaneously 
undergoing  commutation  under  different  brushes,  so  that  the  inter- 
linking field  will  be  produced  by  both  these  conductors  or  coil-sides 
in  the  one  slot. 

Thus— 

Lines  per  amp.  turn,  reckoning  1        .A      ,,       ,,        c      ,      ... 
neighbouring  coils  }  =  40  nefc  lenSth  +  6  P°le-pitch 

i.e.f  =  401.  +.6PP 

This,  however,  is  only  true  under  the  condition  that  the  brush- 
width  =  1  segment,  i.e.  No.  of  coils  short  circuited  by  brush  =  1. 
If  the  brush  short  circuits  g  coils,  then— 

/  =  (40  1.  +  6  PP)g 

The  coefficient  of  self-induction  is  thus  reduced  to  terms  of  the 
armature  dimensions. 

It  may  be  objected  that  the  above  calculation  is  too  rough  to  be 

reliable.  As  a  matter  of  fact,  however,  it  gives  results  accurate 

*  See  Journ.  Inst.  E.E.,  vol.  31,  p.  189. 


COMMUTATION 


123 


enough  for  ordinary  work.  The  value  of  /  is  that  for  coils  in  slots 
lying  in  the  interpolar  spaces,  and  when  the  interpole  shoe  is  brought 
near  to  these  it  naturally  increases  the  value  of  Lc.  This  increase 
depends  on  the  dimensions  of  the  shoe  and  on  the  length  of  the  gap. 
It  may  be  calculated  either  by  means  of  Carter's  formula  (p.  47), 
or  a  conventional  allowance  may  be  made  to  which  a  fair  approxi- 
mation is — 

/  =  (50  net  length  +  6  pole-pitch)^ 

In  any  case  the  value  of  e  thus  calculated  will  be  higher  than 
is   actually  required,  because   the   resistance   of  the   brush,  which 


i-o 

0-9 
0-8 
0-7 
0-6 
0-5 
0-4 
0-3 
0-2 
O'l 


0-2         0-3         0-4         0-5 

* 


0-6 


0'8         0-9 


1-0         1-1 


1-2 


FIG.  80.— CURVE  FOB  E.M.F.  COMMUTATION  CALCULATION. 

helps  commutation,  has  been  entirely  neglected.  It  is  better, 
however,  to  have  the  interpole  ampere- turns  a  little  large,  as  by  a 
diverter  rheostat  they  can  be  adjusted  to  suit  exactly  the  working 
conditions. 

To  facilitate  the  calculation  of  e  by  the  above  methods,  Fig.  80  is 
here  given. 

Interpole  Flux. — From  the  equation — 

e  =  2  X  turns  per  armature  coil  x  flux  per  interpole  X  10 ~8  -f-  tc 

the  value  of  the  average  flux  per  interpole  can  be  obtained.  The 
interpole  air-gap  may  be  taken  the  same  as  that  under  the  main 
poles,  and  the  density  at  the  interpole  shoe  as  40,000  lines  per 


i24     CONTINUOUS   CURRENT   MACHINE   DESIGN 

square  inch.  The  ampere-turns  required  for  this  flux  may  then  be 
calculated  exactly  as  for  the  main  magnetic  circuit.  The  interpole 
arc  may  be  taken  wide  enough  to  ensure  the  coil  lying  in  the  field  all 
the  time  its  segments  are  under  the  brush.  The  axial  length  of  shoe 
is  then  fixed  by  the  value  of  the  flux  in  the  pole. 

Interpole  Flux  from  Reactance-voltage. — Many  writers 
calculate  the  interpole  flux  from  the  value  Vr  as  estimated  below. 
The  author  believes  the  method  outlined  above  to  be  more  accurate 
and  quite  as  simple,  though  it  gives  higher  values  than  are  obtained 
usually  from  Vr. 

Ampere-turns  for  the  Interpole. — The  densities  in  the  whole 
of  the  interpole  magnetic  circuits  should  not  be  so  high  as  to  cause 
much  saturation  in  the  various  iron  parts,  or  else  the  interpole 
field  will  not  be  proportional  to  the  interpole  ampere-turns,  i.e. 
to  the  armature  load,  as  for  proper  commutation  it  should  be.  The 
only  part  where  saturation  is  liable  to  occur  is  the  pole  core,  which 
is  usually  a  steel  casting  or  iron  forging,  and  in  which  the  density 
should  not  exceed  100,000  lines  per  square  inch.  In  order  properly 
to  calculate  the  pole  area,  it  is  necessary  that  the  interpole  leakage- 
factor  should  be  carefully  estimated.  This  is  done  exactly  as  for  the 
main  poles,  with  due  attention  to  the  fact  that  practically  leakage 
will  only  take  place  from  the  interpole  to  the  next  pole  of  opposite 
sign.  It  is  usual  to  calculate  this  leakage-factor  for  full-load 
conditions,  and  to  assume  it  constant ;  its  value  is  very  large,  often 
it  is  1-8  (see  p.  209). 

Having  thus  obtained  the  ampere-turns  necessary  to  carry  the 
flux  already  calculated  though  the  magnetic  circuit,  there  must  be 
added  to  them  a  number  of  ampere-turns  equal  to  those  existing  at 
each  pole  of  the  armature ;  for  the  latter,  as  cross  ampere -turns,  act 
in  opposition  to  the  interpole,  and  must  be  neutralized  before  any 
interpole  flux  can  be  set  up. 

Thus  the  total  ampere-turns  for  the  interpole  consist  of  the 
armature  ampere-turns  per  pole  +  the  ampere-turns  necessary  to 
set  up  the  flux  for  the  E.M.F.  e.  The  total  is  usually  not  very 
different  from  T3  times  the  armature  ampere-turns  per  pole.  An 
example  of  the  calculation  of  interpoles  is  given  on  pp.  195  and  209. 
In  machines  where  the  pole-tip  flux  is  relied  upon  for  commutation,  it 
follows  from  the  foregoing  considerations  that  the  field  ampere-turns 
per  pole  must  not  be  less  than  1*3  times  the  armature  ampere- turns 
per  pole ;  but  such  machines  are  now  practically  obsolete. 

Interpole  Loss. — The  watts  expended  in  the  interpoles  depend 
to  some  extent  upon  the  shunt  field  loss  and  the  efficiency  required. 
Usually  like  the  loss  in  compounding  coils,  it  ranges  from  1  per 
cent,  in  small  machines  to  J  per  cent,  in  large  machines. 

Resistance  Commutation. — It  has  been  shown  that  the  current 


COMMUTATION 


125 


in  a  coil  may  be  caused  to  start  from  a  certain  maximum,  decrease, 
pass  through  zero,  and  rise  to  a  maximum  in  the  opposite  direction 
by  using  a  high-resistance  sliding  contact. 

By  moving  the  brush  uniformly  along  we  ought  to  obtain  a  curve 
of  current  change  similar  to  the  one  shown  in  Fig.  81,  known  as  the 
commutation  curve. 

Effect  of  Self-induction. — Self-induction,  however,  which  is 
present  in  all  armatures,  modifies  the  shape  of  this  curve ;  and  since 
the  coils  lie  on  an  iron  core,  the  resistance  of  any  coil  may,  and 
usually  is,  much  smaller  than  its  self-induction. 

Now,  in  the  ordinary  case,  the  current  will  fall,  when  the  coil  is 


,.--CoLl  touches  Brush. 


.  Time  of  Commutation 


Coil  leaves  Jfrusfi.  •  ^_ . . 


FIG.  81.  —  PROCESS  OF  LINEAR  COMMUTATION. 
closed  by  the  brush,  according  to  an  exponential  law.     Thus 


where  r  =  resistance,  and  Lc  =  the  coefficient  of  self-induction  of  the 
coil,  and  C  is  the  value  of  the  current  in  the  coil  just  before  it  is 
closed  by  the  brush.  On  plotting  this  curve,  it  will  be  found  that 
the  current  never  actually  falls  to  zero  ;  and  also  that  the  greater  r 
is  with  respect  to  Lc,  the  smaller  may  be  the  time  necessary  for  a 
given  fall  of  current. 

Similarly,  the  current  in  an  inductive  circuit  takes  a  definite  time 
to  rise  :  its  value  at  any  instant  being  given  by  the  equation  — 


^representing  the  maximum  current  in  the  coil. 

*  Cf.  Appendix  V. 


126    CONTINUOUS   CURRENT   MACHINE   DESIGN 

Thus  if  the  coil  has  a  large  inductance,  the  natural  time  taken 
to  fall  to  zero  and  rise  to  a  maximum  again  is  correspondingly  large. 

If  the  natural  time  taken  to  fall  and  rise  again  is  greater  to  any 
extent  than  the  time  the  segment  is  under  the  brush,  the  current 
will  tend  to  How  from  the  segment  to  the  brush  as  an  arc  or  spark. 
Hence  it  is  essential  for  resistance  commutation  that  the  resistance 
of  the  coil-circuit  be  large  and  its  self-induction  small. 

This  leads  to  the  high  resistance  brush,  i.e.  the  carbon  brush. 

It  also  limits  us  to  drum-armatures  as  the  self-induction  of  a 
ring-winding  is  so  much  greater.  In  ring-winding  there  is  a  good 
magnetic  path  for  any  leakage  flux  set  up  by  commutation,  and  the 
number  of  turns  is  the  number  of  surface  conductors;  whereas  in 
drum-winding  half  the  path  is  through  air  and  the  number  of  turns 
is  half  the  number  of  surface  conductors.  The  following  are  the 
desiderata  for  successful  resistance  commutation  :— 

(1)  At  the  instant  at  which  the  brush  unites  two  segments  the 
current  which  flows  across  the  small  section  of  brush-tip  must  not 
be  large  enough  to  cause  the  tip  to  get  very  hot  or  to  glow.* 

y 

(2)  The  ratio  =r-  for  the  short-circuit  must  be  such  as  to  give  the 

-L<c 

current  sufficient  time  to  die  away  before  the  coil  leaves  the  brush. 

(3)  At  the  instant  when  the  coil  is  unshort-circuited,  the  current 
passing  from  the  brush  to  the  segment  leaving  the  brush  must  be 
small  enough  to  prevent  heating  or  sparking  at  the  brush-tip.* 

In  the  above  expressions  r  refers  to  the  complete  resistance  of 
short-circuit,  i.e.  armature-coil,  contact,  and  brush,  of  which  the 
contact  forms  by  far  the  greater  part. 

It  is  not  only  necessary  to  limit  Lc,  for  commutation  depends 
upon  the  voltage  set  up  by  the  current,  i.e.  upon  Lc  x  ~c  X  Cw. 

Thus  we  must  limit  this  product  rather  than  any  component ;  and 
of  these  factors  Lc  for  a  particular  kind  of  winding  and  armature  may 
be  considered  constant. 

Assuming,  then,  LC  constant  and  neglecting  minor  factors,  the 
curve  of  current  change  is  represented  very  roughly  by  the  graph 
shown  (Fig.  74).  By  means  of  the  oscillograph  the  actual  current 
variation  has  been  obtained  for  various  cases,  and  has  been  found  to 
be  very  irregular. 

Reactance  Voltage. — The  value  of  e  calculated  above  for  E.M.F. 
commutation  is  a  reactance  voltage  in  the  coil  under  commutation. 
Although  it  is,  as  the  author  thinks,  a  better  guide  to  excellent 
commutation  than  that  presently  to  be  defined,  yet  it  does  not 

*  For  an  excellent  discussion  of  the  current-density  at  the  brush  during  com- 
mutation, the  reader  is  referred  to  the  article  by  F.  W.  Carter  in  the  Elec.  World 
(N.Y.),  March  31,  1910. 


COMMUTATION  127 

so  easily  lend  itself  to  embodiment  in  the  main  design  equations. 
Now,  Hobart  has  suggested  that,  as  the  shape  of  the  curve  of  current 
change  is  so  irregular  and  uncertain,  we  may,  for  comparative 
purposes,  assume  it  to  be  a  half  sine- wave,  and  calculate  the  reactance 
voltage  from  this.  It  has  also  been  suggested,  with  more  reason,  that 
if  we  are  to  make  crude  assumptions  the  graph  might  be  taken  as  a 
straight  line. 

Below,  the  reactance  voltage  is  calculated  for  both  these 
assumptions. 

Let  t.p.s.  =  turns  per  segment,  i.e.  turns  per  armature  coil. 

Then  Lc  =  —         ~Tn» — 
Pteactance  x  =  27r~cLc 
where  ~c  =  frequency  of  commutation 

=  —  (p.  118) 

Sn(4:Ql  +  6  Pp)  x  (t.p.s.)2 

.*.  reactance  =  TT rrfo 

108 

If  Cw  =  current  carried  by  any  armature  coil, 

then  reactance  voltage  =  Cwx 

and  reactance  voltage  per  commutator  segment  = 


where  V/t  =  reactance  voltage  according  to  Hobart,  i.e.  assuming  a 
sinusoidal  change  of  current. 

For  a  straight-line  graph  the  reactance  voltage  is  denoted  by  Vr. 

v  2      2CJSw(4(M  +  6Pp)(t.p.s.)2 

vr  =  v*x-~  -jga- 

Example.—  Armature  net  length  =  5  inches. 

Length  of  mean  turn  =  40  inches. 

Current  reversed  per  section  =  100  amps. 

Frequency  of  commutation  =  500. 

Turns  per  segment  =  1. 

Width  of  brush  =  3  segments,  i.e.  turns  short  circuited  =  3. 

Find  the  reactance  voltage. 

We  have  —  & 

X  (40Z  +  GP^Xt.p.s.)  X  O, 


net  length  =  5" 

L.M.T.a  =  40"     .'.  free  length  =  30" 
i.e.  ?   =    °-  =  10" 


128     CONTINUOUS   CURRENT   MACHINE   DESIGN 

T,       v        nSn  X  (200  +  60)(1)2  X  100 
inus  v/j,  =  -  -  -.Q8 

~c  =  500  =  ^     /.  Sn  =  500  X  2#  =  3000 

.  __  7r3000x  (260)xlOO  _ 

108 
Output  and  Linear  Reactance  Voltage. — If  in  the  formula 

9P    ^    f'f  r»  <a  "\  T7P 

for  Vr  we  substitute  the  value  — ^-r^8          =  "~i a~          ~f  ' 

10b  poles  x  flux  per  pole 

which  is  derived  directly  from  the  E.M.F.  equation,  we  get  the  form — 
v    _  EC(40Z  +  6p.p.)(t.p.s.)* 

poles  x  flux  per  pole 

in  which  EC  stands  for  the  total  watts  generated  in  the  armature. 
This  equation  is  extremely  useful,  as  will  be  seen  later. 

Machine  Dimensions  and  Reactance  Voltage. t — It  has 
been  already  pointed  out  (p.  6)  that  a  field-pole  approximating  to 
a  circular  or  a  square  section  will  usually  give  economical  results ; 
or,  at  the  very  least,  these  shapes  form  a  good  starting-point  for 
comparative  estimates  of  different  designs.  From  this  assumption  it 
is  easy  to  show  that  with  normal  magnetic  densities  there  is  a 
distinct  connection  between  size  of  pole  and  diameter  of  armature ; 
which  connection  has  been  shown  on  p.  20  to  be — 

~D  =  ^.~\  for  round  poles 

If  for  X  we  substitute  the  mean  value  I1 15,  and  insert  in  the 
formula  for  Vr  after  some  transformation,  f  we  obtain  the  equations — 

O  Z?  J      /A.  «.  «  \Q     C*  /~] 

^r  OUCu  .  (t.p.S.)   .  b%  .  L/w  /.          .         i  i 

Vr  =  -  r    3 for  circular  poles 

,  ,7        93d.  (t.p.s.)2.  Sn.Cw. 
and  Vr  =  -  ip ~  f°r  square  poles 

where  C»  is  the  current  in  any  armature  turn,  d  is  the  diameter  or 
length  of  side  of  the  pole,  as  the  case  may  be. 

Machine  Output,  Dimensions,  and  Reactance  Voltage. — 
Going  a  step  further,  we  may  express  the  output  in  terms  of  the 
reactance  voltage  and  flux  (see  Appendix  VI.).  We  then  get  the 
forms — 

A.  For  multiple-circuit  windings— 

(1)  Vr  =  0-55  X  K.W.  per  pole  x  t.p.s  -f-  pole  diameter  for  circular 

poles. 

(2)  Vr  =  0-465  x  K.W.  per  pole  x  t.p.s  -f-  pole  side  for  square  poles. 

*  "  Flux  per  pole  "  in  these  formulae  is  obviously  the  useful  flux  per  pole,  i.e.  in 
the  armature. 

t  See  Appendix  VI.  J  See  Appendix  VI. 


COMMUTATION  129 

B.  For  two-circuit  windings  with  two  brush  rows — 

(1)  Vr  =  0-275  K.W.  x  t.p.s.  4-  pole  diameter  for  round  poles. 

(2)  Vr  =  0-232  K.W.  X  t.p.s.  -i_  length  of  pole  sides  for  square  poles. 

These  formulae  are  of  great  assistance  in  determining  the  limiting 
dimensions  for  preliminary  designs.  They  have,  however,  limits 
themselves.  For  reference  to  p.  122  will  show  that  the  value /was 
obtained  on  the  assumption  that  all  the  g  coils  undergoing  com- 
mutation lay  in  the  same  slot.  This,  with  ordinary  brush  widths,  is 
the  case.  But  if  the  brush  width  be  increased  so  that  g  is  greater 
than  the  number  of  coils  per  slot,  the  reactance  voltage  per  segment 
is  not  further  increased.  Thus  Vr  has  its  maximum  value  when  g  = 
the  coils  per  slot.  And  in  those  rare  cases  when  g  is  greater  than  the 
number  of  coils  per  slot,  the  latter  value  is  to  be  adopted  in  the 
calculation  in  place  of  g.  We  say  "  those  rare  cases,"  because  they 
only  occur  when  either  the  number  of  slots  is  abnormally  large,  or 
the  width  of  brush  so  great  as  to  endanger  sparking,  on  account  of 
the  fact  that  some  of  the  coils  will  be  well  under  one  pole-tip  or  the 
other,  while  their  segments  are  still  under  the  brush. 

Limits  of  Linear  Reactance  Voltage. — Properties  of  Brushes. 
— The  limits  to  be  set  to  the  reactance  voltage  depend  upon  the  quality 
of  the  brush  used.  Senstius  *  has  shown,  and  the  author's  experience 
confirms  the  view,  that  the  reactance  voltage  which  a  brush  of  given 
quality  will  stand  without  sparking,  is  inversely  as  the  current 
density  at  which  the  brush  may  be  safely  worked.  Thus  the  pro- 
duct Vr  x  current  density  is  a  constant,  and  usually  has  a  value  of 
about  55.  This,  however,  depends  to  some  extent  upon  the  pressure 
employed  to  keep  the  brush  up  to  the  commutator  face;  for  the 
contact  resistance  varies  both  with  this  and  with  the  current  density. 
With  ordinary  grades  of  carbon  brush  the  pressure  employed  should 
be  about  1  \  Ib.  to  1J-  Ib.  per  square  inch ;  but  with  brushes  made  of 
almost  pure  graphite  the  pressure  may  be  considerably  increased,  up 
to  3  or  even  4  Ibs.  per  square  inch,  because  the  material  of  the  brush 
forms  a  natural  lubricant.  Fig.  82  shows  the  variation  of  properties 
due  to  changing  pressure  of  the  well-known  Morganite  '  Link '  1  brush 
which  is  so  constructed  as  to  have  a  high  resistance  across  the  brush 
face,  but  a  low  resistance  lengthwise.  Fig.  83  shows  a  curve  at 
1 J  Ib.  per  square  inch  for  the  Battersea  carbon  brush,  type  C,  which 
is  a  first-rate  grade  of  hard  carbon  brush.  With  special  brushes, 
such  as  Morganite,  the  value  above  given  for  the  product  of  Vr  and 
current  density  will  not,  of  course,  hold,  but  they  should  be  judged 
from  curves  such  as  Fig.  82.  The  following  table  of  well-known 
English  and  American  brushes  gives  the  makers'  estimate  of  current 

*  Proc.  Amer.  I.E.E.,  vol.  24,  p.  420;  see  also  Carter's  paper  in  Elec.  World 
(N.Y.),  March  31,  1910. 

K 


130     CONTINUOUS   CURRENT   MACHINE   DESIGN 


Fr 
Di 
Te 

Tti 

MORQANITE    BRUSHES. 

Contact   Resistance  Varying   with    Current  .Density. 

Tests  made  with  ^jgj^jgg  Brush  on  Commutator 

essure  on  Brush  «=  3  Ibs.  per  square  inch, 
rection  of  Current  —  from  Brush  to  Commutator 
mperature  of  Commutator  kept  constant  at  -if?  Centigrade 
is  Curve  holds  for  peripheral  speeds  up  to  10,000  ft.  per  minute 

'  '4 

I'Z 

1 

\\ 

1 

V 

\ 

I 

\\ 

'•°      § 

V 

\\ 

\ 

O'S   "§ 

\v 

\ 

•x 

^ 

s 

0-6    § 

' 

X 

\ 

x 

[ 

x 

X 

s 

-9- 

3 

v 

V 

^ 

"^v. 

^ 

^ 

S. 

b^ 

-^. 

'  —  - 
~> 

~^_ 
—  *^, 

T~- 
—  -~, 

—  — 

~^= 
. 

•  —  . 

•"•"^ 

-  —  *- 

= 

— 

^ 

^ 

== 

== 

^ 

O'2 
O't 

20          30          40  50          60  70  80          go          100         no 

Current  Density  in  Brush  in  Amperes  per  square  inch 
Curve  X.  =  Pressure  drop  with  a  pressure  of  3  Ibs.  per  square  inch  on  Brush. 

„       Y  =  Contact  Resistance  with  a  pressure  of  3  Ibs.  per  square  inch  on  Brush 
'    .,       a^         .,  ..  .,  ,,  2    ,,  ,,  .,      • 

.,       b=         „  „  .,  ,.  4    „ 

FIG.  82. 


BATTERSEA   CARBON    BRUSHES. 

Contact   Resistance   Varying  t;ith   Current   Density- 

Tests  made  with  3lO§C  Brush  on  Commutator. 
~  *%y" 
Pressure  on  Brush  =  tj  Ibs.  per  square  inch. 
Direction  of  Current—  from  Brush  to  Commutator. 
Temperature  of  Cpramutator  kept  constant  at  26°  Centigrade 

I 

1 

\\ 

\\ 

\\ 

\ 

+ 

\ 

^^ 

^* 

~~- 

~*~ 

— 

i 

1? 

— 

-— 

^ 

:  

^ 

\ 

Y 

\ 

A 

\ 

\ 

x 

x 

s^ 

»K 

•>» 

E 

•**. 

*  — 

-  —  . 

^.^ 

"^ 

-— 

•»"^ 

*'  i. 

—  — 

• 

^H— 

-L 



10  20          30          40  50          60          70          80          go          too         no         120         i 

Current  Density  in  Brush  in  Amperes  per  square  inch. 
PRESSURE  DROP  CCRVB.  Y  =  COM  ACT  RESISTANCE  Cm 

FIG.  83. 


COMMUTATION 


density,  together  with  the  author's  estimate  of  the  value  of  Vr  which 
they  will  deal  with  satisfactorily,  and  of  the  coefficient  of  friction, 
and  of  the  pressure  which  should  be  used  with  them  : — 

TABLE  VI. 


Brush. 

Current  den- 
sity, amps, 
per  sq.  inch. 

Vr. 

Coefficient  of 
friction. 

Pressure, 
Ibs.  per 
sq.  inch. 

Battersea  A  

40 

1-4 

0-22 

1-5 

„        B  

45 

1-2 

0-25 

2 

„     c  

30 

1-8 

0-28 

1-5 

Partridge       

35 

1-5 

0-25 

1-5 

National  Columbia 

28 

1-9 

0-28 

1-5 

Le  Valley  Vitse     

25 

2 

0-3 

1-5 

National  Graphitized    .  .  . 

55 

1 

0-22 

2 

Pressure  Drop  due  to  Contact  Resistance. — The  passage  of 
the  current  from  brush  to  commutator  inevitably  produces  a  pressure 
loss,  which,  however,  is  curiously  constant  for  wide  variations  in 
current  density,  as  is  shown  in  the  curves  X  in  Figs.  82,  83.  For 
the  ordinary  range  of  carbon  brushes,  at  their  appropriate  current 
densities,  the  voltage  drop  varies  from  1  to  1*2  volt  according  as  the 
brush  is  of  low  or  high  resistance ;  i.e.  suitable  for  a  low  or  a  high 
value  of  Vr. 

Machine  Dimensions  limited  by  Reactance  Voltage. — The 
formulae  on  p.  128,  taken  in  conjunction  with  Table  VI.,  show 
that,  if  resistance  commutation  be  relied  upon,  the  output  is 
limited  by  the  type  of  brush  adopted.  Thus,  with  circular  poles,  a 
lap-wound  armature,  and  Battersea  C  type  brushes 

^r  ITT  T        pole  diameter  x  1'8  • 

K.W.  output  per  pole  =  £ — .  gr 

0-55  x  t.p.s. 

i.e.  K.W.  output  =  poles  X  pole  diameter  x  3'26 
with  one  turn  per  commutator  section. 
Substituting  pole  diameter  x  poles  =  1*5  D.X  =  T72  D 

.  ^      K.W. 
we  get  D  = 


or,  for  square  poles,  D 


5-6 
K.W. 
~475 


with  average  magnetic  densities. 

These  formulae,  it  must  be  remembered,  are  derived  from,  and 
dependent  upon,  certain   magnetic   densities.     By  forcing  up   the 


132     CONTINUOUS   CURRENT   MACHINE    DESIGN 

densities,  the  denominator  in  the  above  fractions  may  be  in- 
creased. The  average  value  for  machines  of  about  200  K.W.  would 
be,  according  to  makers'  catalogues,  about  6'5 ;  but  for  100  K.W.,  5'5 
would  seem  to  be  about  the  usual  figure. 

It  will  be  noticed  that  the  speed  does  not  enter  the  above 
equations,  so  that  it  is  impossible  to  compare  the  formula  directly 
with  the  limiting  values  worked  out  on  pp.  22  and  84,  as  prescribed 
by  other  conditions.  If  we  work  out  the  concrete  case  on  pp.  23  and 
85  under  these  conditions,  it  will  form  a  fair  comparison. 

Example. — The  machine  is  to  give  200  K.W.  at  500  volts  and  at 
400  r.p.m. 

~       K.W.  ,       .      ,         .          200       OKh7/, 
D  =  -=-=-  for  circular  poles  =  -=-=•  =  35'7 
5'6  5*6 

say  =  35" 

Pole  diameter  x  poles  =  1/72D  =  60 
Whence  with  four  poles 

Pole  diameter  (=  armature  core  length)  =  15" 

D2L  =  18,500 
With  six  poles, 

Pole  diameter  =  10" 

D2L  =  12,200 

Thus  a  six-pole  machine  would  be  cheaper  than  a  four-pole 
machine,  if  resistance  commutation  were  relied  upon  ;  and  in  either 
case  the  machine  is  larger  than  considerations  of  temperature  rise 
alone  would  dictate  (cf.  p.  86).  In  this  way  is  the  choice  of  the 
number  of  poles  influenced  ly  commutation. 

Minimum  Size  for  Large  Generators. — It  has  been  said  that 
increasing  the  magnetic  densities  will  result  in  a  smaller  machine 
for  the  same  reactance  voltage,  and  the  above  example  shows  that 
average  densities  lead  to  greater  armature  dimensions  than  are 
dictated  by  temperature  rise  alone.  These  conditions  have  tempted 
designers  to  force  up  the  magnetic  densities  until  the  size  of  the 
machine,  without  inter-poles,  corresponds  almost  with  the  limiting 
temperature.  There  is,  of  course,  a  limit  to  this,  but  it  is  not  reached 

K  W^ 

before  D  =      '     ',  which  corresponds  to  a  pole-face  density  of  about 
y  *o 

65,000  and  a  value  of  Vr  =  2.  The  advantage  in  the  use  of  inter-poles, 
then,  obviously  consists  in  reduced  densities  and  field  ampere-turns. 
Commutation  Losses.— On  p.  86  the  sources  of  heat  in  the 
commutator  have  been  enumerated.  Since  carbon  brushes  are  now 
universally  adopted,  the  particulars  just  given  of  well-known 
makes  can  be  used  for  estimation  of  the  commutator  losses.  The 
electrical  loss,  for  instance,  can  from  Fig.  83  be  directly  determined, 
since  it  is  the  product  of  the  current  collected  per  brush  arm,  the 


COMMUTATION  133 

number  of  arms,  and  the  pressure  drop  at  the  contact.  Failing  such 
a  curve  to  work  from,  a  good  average  value  for  the  resistance  per 
square  inch  of  contact  surface  is  0*03  ohm. 

The  number  of  square  inches  of  brush  surface  is  dictated  by  the 
current  density  which  can  be  employed  for  the  particular  brush 
selected  ;  so  that  from  these  two  factors  the  watts  lost  electrically  can 
be  computed  as  follows  : — 

Current  per  brush  arm  =  total  current  -£-  number  of  positive 

or  negative  arms 

Area  of  brush  surface  per  arm  =  current  per  arm  ~-  current  density 
Kesistance  of  contact  per  arm  =  0*03  -f-  area  per  arm 

Loss  at  each  brush  arm  =  (current  per  arm)2  x  resistance  per 

arm 

Total  electrical  loss  =  number  of  arms  (+  and  -)  x  loss 
per  arm 

The  electrical  loss,  then,  may  be  expressed  as 

Total  current  X  current  density  at  brush  x  0*06 

but  it  is  better  to  take  it  from  curves  like  Fig.  83.  From  Fig.  83 
it  would  be  2 '4  x  total  current. 

Friction  Losses. — The  coefficients  of  friction  for  the  various 
types  of  brush  are  given  in  Table  VI.  If  Vc  be  the  peripheral 
velocity  of  the  commutator  surface  in  feet  per  minute,  the  friction 
loss  is,  in  watts — 

746 
Brush  pressure  per  sq.  in.  x  total  brush  area  x  coefft.  X  Vc  X  QQnnn 

ooUUU 

.  r        2  X  total  current  n  nnnr*  TT  i».     *  *  •  *.- 

=  1-5  -  — T—          -T-  x  0-0226  Vc  x  coefft.  of  friction 

current  density  in  brush 

if  1J  Ib.  per  sq.  inch  be  allowed ;  and  this  is 

A  nr.o  total  current  Tr  „,,     „«.  ,. 

=  0-068  -         — , rr— *— T — r  X  Vc  X  coefft.  of  friction 

current  density  in  brush 

or,  assuming  30  amperes  per  sq.  inch  as  the  brush-current  density, 
Friction  loss  =  0-00226  x  total  current  X  Vc  x  coefft.  of  friction. 

When  the  brush  constants  are  accurately  known,  curves  like  those 
of  Fig.  84  can  be  constructed,  from  which  the  losses  can  be  read  off 
at  once. 

Commutator  Dimensions. — Adding  together  the  electrical  and 
friction  losses,  the  cylindrical  area  of  the  commutator  face  is  im- 
mediately determined,  as  shown  on  p.  86,  from  temperature  rise 
limits ;  whence  the  product  diameter  X  length  of  face  is  obtained. 
The  value  of  diameter  and  face  length  are  then  dependent  upon  the 
following  considerations : — 

1.  The   weight   of  the   commutator   should  be   as   small   as  is 


134    CONTINUOUS   CURRENT   MACHINE   DESIGN 

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and  2  inches,  according  to  the  commutator  diameter.     It  follows  that 
the  commutator  diameter  should  be  as  small  as  possible. 

2.  The  diameter  of  the  commutator  should  be  less  than  the  diameter 
of  the  armature  measured  at  the   bottom  of  the  slots.     It  must, 


COMMUTATION  135 

however,  be  great  enough  to  allow  of  a  minimum  thickness  per 
segment  of  at  least  0*15  inch  +  an  insulation  thickness  of  0'03  inch. 

3.  The  axial  face-length  is  frequently  determined  by  the  brush 
collecting  surface  independently  of  temperature  rise ;  for  if  the  number 
of  segments  to  be  covered  by  one  brush  be  fixed,  the  length  of  the 
commutator  varies  directly  as  the  current  to  be  collected. 

Number  of  Segments  covered  by  the  Brush. — This  is  a 
question  that  has  never  been  satisfactorily  settled.  The  author 
usually  limits  it  to  the  number  of  coils  per  slot.  If  the  brush  cover 
too  many  segments,  bad  contact  ensues ;  or  sometimes  the  coil  is  so 
long  a  time  under  the  brush  as  to  cause  it  to  enter  well  under  the 
pole-tip  before  it  is  thrown  into  circuit  again,  and  in  these  circum- 
stances good  commutation  is  almost  impossible.  On  the  other  hand, 
the  brush  should  be  at  least  as  wide  as  one  commutator  section.  In 
practice,  the  average  number  of  segments  covered  is  three,  and  the 
average  brush  thickness  is  about  f  inch  (cf.  p.  169). 

Number  of  Brushes  per  Arm. — There  should  not  be  less  than 
two  brushes  per  arm.  An  accident  to  one  does  not  then  throw  the 
machine  out  of  service.  Too  great  an  axial  length  per  brush  means 
poor  contact.  An  axial  length  of  1  inch  to  1  £  inch  per  brush  is  usual. 

Various  Commutation  Limits.— Besides  sparking  due  to  too 
heavy  a  reactance  voltage,  various  other  troubles  may  appear  in 
machines  made  without  inter-poles.  Of  these  the  chief  are:  (1) 
Glowing  of  the  brush  tip  due  to  excessive  current  density  there.  (2) 
Spitting,  which  consists  of  little  explosive  sparks  appearing  oc- 
casionally. (3)  Picking  up  copper  by  the  brush.  The  first  seems  to 
be  avoided  if  the  armature  ampere-turns  per  pole  do  not  exceed  6500. 
The  second  is  apparently  a  faint  effect  of  reactance-voltage  combined 
with  heavy  armature-reaction,  and  can  therefore  be  avoided.  The 
third  is  avoided  by  keeping  the  brush  to  its  proper  density  in 
amperes  per  square  inch. 

Example  of  Commutator  Design.— 200  K.W.,  500  volt,  400 
r.p.m.,  six-pole  lap-wound  generator ;  without  inter-poles. 

Diameter  of  armature  =  35". 

Maximum  convenient  diameter  of  commutator  =  30". 

Peripheral  speed,  assuming  28"  diameter,  2940  ft.  per  min. 

Electrical  loss  (p.  133)  =  2-4  X  400  =  960  watts. 

Coefficient  of  friction  =  0*3. 

Friction  loss  (p.  133)  =  0-00226  X  400  x  2940  X  0'3  =  800  watts. 

Total  losses  =  1760  veks;  u>OX«. 

Cylindrical  surface  =  440  sq.  in. 

Diameter  X  length  =  140  sq.  in. 

Face  length  from  temperature  rise  =  5". 

Number  of  segments  possible  ^  =  488. 


136     CONTINUOUS   CURRENT   MACHINE   DESIGN 

Width  of  brush  =  £". 

Amperes  per  arm  =  133. 

Brush  area  per  arm  (with  current  density  =  30)  =  4*4  sq.  in. 

Axial  length  of  brushes,  4 -4  X  f  =  5'9". 

Axial  length  of  face,  allowing  for  six  brushes,  each  1"  long  with 
clearances  =  8". 

Thus  in  this  instance  the  commutator  face  length  is  determined 
by  the  current  to  be  collected  rather  than  by  the  surface  necessary 
for  radiating  purposes. 


CHAPTER  X 
INSULATION 

Insulating  Materials. — It  is  an  unfortunate  fact  that  those  materials 
which  are  most  effective  as  insulators  usually  lack  some  mechanical 
quality,  such  as  toughness  or  flexibility.  In  consequence,  to  meet 
the  conditions  of  dielectric  and  mechanical  strength,  the  insulation 
adopted  must  usually  be  composite;  i.e.  made  up  of  two  or  more 
materials,  one  chosen  for  mechanical  strength,  the  other  for  dielectric 
strength. 

I.  Insulators  with  Good  Mechanical  Qualities. — Of  materials 
possessing  the  former  qualification,  especially  toughness,  the  chief 
are :  the  various  forms  of  fibrous  or  cellulose  material,  such  as  paper, 
press-board,  fullerboard,  press-spahn,  vulcanized  fibre,  cotton  fabrics, 
and  so  on.  None  of  these  materials  has  a  very  high  dielectric  strength, 
because  they  all  absorb  moisture  to  some  extent,  and  most  of  them 
are  easily  damaged  by  high  temperature.  Some  idea  of  their  relative 
dielectric  values  may  be  gleaned  from  the  following  table  of  dis- 
ruptive strengths,  i.e.  of  alternating  electrical  pressure  with  a 
sinusoidal  wave-form  at  which  puncture  occurs: — 

TABLE  VII. 


Dry  material,*  0-04" 
thick. 

Disruptive  strength 
(R.M.S.  volts). 

Brown  paper    . 

7,000 

Eed  rope  paper 

6,800 

Express  paper  . 

7,000 

Manila  paper  . 

6,000 

Press-spahn 

9,000 

Horn  fibre 

12,000 

Vulcanized  fibre 

6,000 

Dry  wood  (maple)    . 

600 

*  Dried  in  a  vacuum  oven  for  four  hours  at  75°  C.,  and  tested,  when  cold,  within 
half  an  hour  afterwards.    Compare,  however,  Electrician,  1905,  p.  949. 


138    CONTINUOUS   CURRENT   MACHINE   DESIGN 

Besides  the  use  of  cotton  for  covering  wires,  which  is  referred  to 
more  fully  a  little  later,  various  cotton  and  flax  fabrics  are  made  up 
and  impregnated  for  use  as  insulating  materials.  These  are  broadly 
spoken  of  as  varnished  linen,  varnished  long  cloth,  varnished  canvas, 
and  so  on.  Many  are  sold  under  special  trade-names,  such  as 
Empire  cloth,  etc.  They  are  very  effective  as  insulators,  and  are  nearly 
all  prepared  by  drying  the  woven  fabric  in  a  vacuum  oven  and 
steeping  it  in  the  varnish ;  afterwards  the  excess  varnish  is  drained 
off,  and  the  material  dried  in  a  stove  to  which  an  ample  supply  of  air 
is  supplied  to  oxidize  the  varnish  thoroughly.  Such  preparations 
have  a  disruptive  strength  of  from  7000  to  10,000  volts  (R.M.S.)  in 
the  case  of  sheets  10  mils  thick. 

Too  much  stress  must  not  be  laid  upon  the  value  of  the  disruptive 
strength,  for  so  much  depends  upon  the  exact  test  conditions  that  the 
figures  are  more  valuable  relatively  than  actually.  In  all  the  tests 
given  above,  moisture  was  driven  out  before  test ;  for,  since  there  is  not 
one  of  the  materials  in  the  whole  list  which  does  not  absorb  moisture 
to  some  extent,  all  before  use  should  be  dried  and  impregnated 
with  some  insulating  varnish.  This  treatment  may,  or  may  not, 
considerably  increase  the  disruptive  strength  measured  under  average 
atmospheric  conditions,  but  there  is  no  questioning  the  enormous 
increase  in  safety  under  ordinary  working  conditions.  The  increase 
in  the  disruptive  strength  of  red  rope  paper,  for  instance,  seems  to  be 
at  least  70  per  cent.,  while  that  of  press-spahn  is  little  changed  ;  yet 
for  practical  safety  both  require  impregnating. 

Again,  the  duration  of  the  test  has  much  to  do  with  the  dis- 
ruptive strength.  For  if  the  test  pressure  be  left  on,  it  almost 
always  sets  up  local  heating,  which  causes  the  material  to  break 
down  at  a  much  lower  value  than  is  shown  in  the  table.  Thus  an 
increase  of  temperature  of  30°  C.  has  been  known  to  reduce  the 
dielectric  strength  50  per  cent. 

Varnishes. — For  impregnating  cellulose  and  other  materials 
many  excellent  varnishes  are  obtainable.  Most  of  these  seem  to  be 
founded  upon  boiled  linseed  oil,  and  there  is  considerable  divergence 
of  opinion  as  to  the  desirability  of  this  compound  on  account  of  the 
possible  presence  of  acid.  The  varnish  known  as  (l  Armalac  "  seems 
to  be  free  from  linseed  oil,  and  is  said  to  be  a  solution  of  paraffin  wax 
of  a  specially  high  melting-point.  If  this  be  the  case,  it  overcomes 
many  of  the  disadvantages  of  other  varnishes,  and  the  author  has 
certainly  found  it  very  satisfactory.  Examples  of  the  use  of  these 
varnishes  are  given  later  in  connection  with  typical  insulation 
arrangements.  Shellac  varnish  is  now  almost  entirely  given  up 
because  of  its  inflexibility  when  dry. 

II.  Insulators  with  Very  High  Dielectric  Strength.— Of 
materials  possessing  a  high  dielectric  strength,  but  poor  mechanical 


INSULATION  139 

qualities,  the  best  known  is  "  mica."  Many  varieties  of  this  mineral 
are  found,  differing  from  one  another  in  colour,  hardness,  and 
insulating  properties.  The  disruptive  strength  for  plates  0'04  inch 
thick  appears  to  be  from  20,000  to  200,000  E.M.S.  volts,  so  that  its 
capacity  for  resisting  breakdown  is  very  high.  It  is  further  practi- 
cally fire-proof,  and  suffers  only  from  its  brittleness  and  liability  to 
come  away  in  thin  laminae  or  flakes.  To  overcome  this,  it  is  made 
up  into  various  special  forms  by  being  cemented  on  to  a  backing,  as 
mica-paper,  mica-longcloth,  mica- canvas.  It  is  also  made  up  with 
shellac  or  other  cement  into  "  micanite,''  and  as  such  may  be  moulded 
while  hot  into  almost  any  desired  form. 

These  mica  preparations  are  excellent  insulators,  having  disruptive 
strength  somewhat  as  follows  : — 

TABLE  VIII. 


Material  made  up  to 
0-04"  thick. 


Micanite 
Mica-canvas    . 
Mica-longcloth 
Mica-paper 


Disruptive  strength  (R.M.S. 
volts). 


30,000 

2,500 
2,500 
15,000-20,000 


Porcelain  is  another  fire-proof  material  possessing  high  dielectric 
strength,  but  because  of  its  brittleness  it  is  only  suitable  for  such 
purposes  as  bushes,  fuse  handles,  and  the  like.  Asbestos  is  a  fair 
insulator,  and  also  fire-proof,  but  it  is  very  friable ;  it  is  used,  as  will 
be  seen  later,  for  field-coils,  but  requires  impregnation  to  render  it 
satisfactory. 

Many  rubber  compounds  are  used,  such  as  vulcanite  and  ebonite. 
These,  especially  the  latter,  are  excellent  insulators ;  but  they  suffer 
from  the  disadvantage  that  if  made  flexible  they  soften  at  a  very  low 
temperature,  and  if  made  hard  they  are  usually  brittle. 

Insulation  of  Round  Wires. — Insulated  wire  is  made  by 
spinning  over  the  wire  a  coating  of  cotton  or  silk.  Cotton-covered 
wires  are  made  in  three  grades :  (1)  single  cotton  covered  (S.C.C.), 
(2)  double  cotton  covered  (D.C.C.),  (3)  fine  double  cotton  covered. 
Triple-covered  wire  is  also  made  for  special  purposes.  Silk-covered 
wires  are  used  in  practice  with  a  double  covering  only.  The  allow- 
ances for  thickness  of  these  coverings  vary  with  the  diameter  of  the 
wire  itself,  but  may  generally  be  taken  as  follows  : — 

1.  S.C.C.— For  all  sizes  to  No.  20  S.W.G.  add  to  the  diameter 
of  the  wire  5  mils. 


140    CONTINUOUS   CURRENT   MACHINE   DESIGN 

Nos.  19  to  13  S.W.G.,  add  8  mils. 

Nos.  12  and  larger,  add  10  mils. 

Double  Cotton  Covered  (ordinary). — For  all  sizes  to  No.  18 
S.W.G.,  add  to  the  diameter  of  the  wire  10  mils. 

Nos.  17  to  13,  add  12  mils. 

Nos.  12  and  larger,  add  14  mils. 

Fine  Double  Cotton  Covered.— All  sizes  to  No.  20  S.W.G.,  add  6  mils. 

Nos.  19  and  18,  add  8  mils. 

Nos.  17  to  13,  add  10  mils. 

No.  12  and  larger,  add  12  mils. 

A  double  silk  covering  adds  from  4  to  8  mils  to  the  diameter  of 
the  wire  according  to  size. 

It  is  evident  that  where  the  coil  consists  of  a  large  number  of 
fine  wires  (as  in  high-voltage  machines),  a  much  higher  space-factor 
may  be  obtained  by  using  the  fine  D.C.C.,  or,  in  special  cases,  silk 
covering ;  and  the  extra  expense  entailed  is  often  more  than  compen- 
sated for  by  the  larger  output  obtained. 

Wire  manufacturers  are  usually  willing  to  vary  the  covering  to 
quite  a  considerable  extent  to  suit  special  requirements,  but  of  course 
it  is  difficult  then  to  carry  a  reasonable  stock. 

Heavy  wires,  rectangular  conductors,  and  strip,  are  usually  covered 
with  a  fine  close  braiding,  which  is  in  general  from  5  to  8  mils  thicker 
than  ordinary  double  lapping.  Sometimes  a  double-cotton  covering 
is  used  as  well,  inside  the  braiding  (cf.  p.  206). 

(Jh,oice  of  Coverings. — For  field-coils  with  a  voltage  of  not  more 
than  100  per  coil,  S.C.C.  is  usually  good  enough,  particularly  if  the 
coil  be  thoroughly  impregnated  after  winding. 

For  armatures  D.C.C.  should  always  be  used. 

Space-factor. — The  ratio  of  the  nett  sectional  area  of  the  copper 
in  an  armature  slot  to  the  actual  area  of  the  slot  is  called  the  space- 
factor.  Similarly,  in  the  case  of  coils,  if  a  right  section  be  taken 
through  the  coil,  the  ratio  of  the  space  occupied  by  the  copper  to  that 
occupied  by  copper  and  insulation  together  is  called  the  space-factor. 
Thus  in  Fig.  44  the  space-factor  of  the  coil  is 

Number  of  turns  X  sectional  area  of  wire 
lc  X  dc 

The  space-factor  is  thus  a  measure  of  the  utilization  of  the  winding- 
space,  and  cannot  be  greater  than  unity.  The  object  of  the  designer 
should  be  to  get  the  space-factor  up  without  lowering  the  dielectric 
strength,  and  this  can  only  be  achieved  by  most  careful  and  scientific 
use  of  insulating  material.  Naturally  the  space-factor  will  depend 
not  only  upon  the  method  of  winding,  but  also  upon  the  size  and 
sectional  shape  of  the  wire  used.  Strip  will  give  a  higher  space- 
factor  than  round  wire,  and  a  low-voltage  coil  will  have  a  higher 


INSULATION  141 

space-factor  than  a  high-voltage  coil.  For  preliminary  calculations 
a  knowledge  of  the  probable  space-factor  is  especially  useful. 

Space-factor  of  Field  Coils. — This  will  obviously  depend  upon 
the  type  of  coil  used.  Broadly  speaking,  two  types  only  are  made  ; 
in  the  one  case  the  wire  is  wound  upon  a  spool  of  metal,  or 
of  some  special  material,  and  in  the  other  case  the  coil  is  wound 
and  taped  without  any  spool.  These  two  types  have  already  been 
illustrated  in  Figs.  41  and  43,  p.  73.  The  second  form  is  the  cheaper 
to  make,  and  usually  occupies  less  room ;  but,  as  already  shown,  it 
does  not  so  readily  dissipate  the  heat  generated  in  it. 

For  shunt  field-coils  the  space-factor  ranges  from  0'2  in  the 
case  of  a  high-speed  motor  of  500  volts  and  2  H.P.  up  to  0*6, 
or,  in  exceptional  cases,  07  in  the  case  of  large  generators  for 
200  volts. 

When  the  space-factor  is  as  low  as  0'2  it  usually  pays  to  raise  it 
by  adopting  wire  with  a  special  covering. 

Series  coils  having  fewer  turns  of  larger  cross-section  naturally 
have  a  much  higher  space-factor,  and  a  value  as  high  as  0*75  may 
sometimes  be  obtained  by  winding  copper  strip  edgewise. 

Examples  of  Field-Coil  Insulation. — Since  it  is  impossible  to 
lay  down  any  hard-and-fast  rule  as  to  the  arrangement  of  the 
insulating  material  about  a  field  coil,  the  only  course  is  to  give  for 
guidance  reliable  examples  of  modern  practice.  The  whole  subject  of 
insulation  is  but  in  its  infancy,  and  careful  study  of  it  will  well  repay 
any  manufacturer  of  electrical  machines.  Below  are  cited  instances 
of  each  of  the  two  main  types  of  coil  previously  referred  to,  and  of 
the  details  of  modern  railway-  and  tramway-motor  coils,  which  often 
receive  rough  treatment. 

Example  1.— Metal  Spool  (Figs.  41  and  42).— The  spool  is  lined 
with  varnished  press- spahn  10  mils  thick,  strengthened  by  one  layer 
of  empire  cloth  5  mils  thick  in  machines  for  440  volts  and  over. 
Strips  of  tape  f ' '  wide,  zigzagged  in  and  out  of  the  last  layers,  are 
employed  to  fix  the  outer  turns,  and  the  inner  end  is  brought  up  a 
special  groove  or  hole  made  in  the  spool  (cf.  Fig.  131).  The  whole 
finished  coil  is  dried  in  a  vacuum  oven,  and  then  immediately  treated 
with  an  insulating  varnish,  and  afterwards  baked.  Sometimes  a 
special  brass  terminal  is  bound  into  the  coil,  as  in  Fig.  131. 

Example  2.— Taped  Coil  (Figs.  43,  85,  and  124).— These  coils 
are  usually  wound  upon  a  wooden  spool  with  loose  ends,  so  that  when 
completed  they  can  easily  be  removed.  The  turns  are  kept  in  place 
by  zigzag  tapes  throughout,  and  when  removed  from  the  spool  the 
coil  is  usually  lined  with  varnished  press-spahn  to  protect  it  from 
mechanical  abrasion,  and  coil  and  press-spahn  are  then  bound  all 
over  with  tape  about  |"  wide.  The  turns  of  the  tape  are  allowed  to 
overlap  for  about  half  their  width ;  and  two  servings  are  put  on,  one 


142     CONTINUOUS   CURRENT   MACHINE   DESIGN 

as  a  right-hand  spiral,  the  other  as  left-hand  spiral,  so  that  they 
mutually  interlock.  The  completed  coil  is  dried  in  a  vacuum  oven, 
treated  with  insulating  varnish,  and  baked,  the  three  processes  being 
carried  out  twice.  The  inner  end  is  brought  out  carefully  and 
specially  protected  by  an  insulating  sleeve. 

Example  3. — Where  much  vibration  is  likely  and  a  high  voltage 
is  used,  as  in  the  case  of  traction-motors,  more  careful  construction  is 
adopted.  Usually  these  machines  are  series  wound,  so  that  the  con- 
ductor is  a  large  wire,  a  cable,  or  a  flat  strip ;  and  often  it  is  necessary 
to  render  the  coil  fire-proof.  The  following  instructions  for  such 
coils  exemplify  methods  commonly  adopted. 

Railway  -  Motor  Field -Coils.  Fire-proof  Construction. 
Strip  Wound. — The  turns  are  insulated  by  winding  between  them 
two  layers  of  asbestos  each  10  mils  thick.  The  coil  is  then  dried 
thoroughly,  well  varnished,  and  pressed  whilst  hot.  Moulded  mica 
corner  and  side  pieces  40  mils  thick  are  placed  on  the  coil  to 
protect  it  and  to  keep  the  turns  from  sliding  over  one  another  ;  and 
farther  protection  is  afforded  by  layers  of  mica  and  asbestos  made 
up  into  washers  about  ^  inch  thick  and  placed  over  the  pole  tip  and 
also  under  the  yoke.  The  ends  of  the  coil  are  usually  thoroughly 
insulated;  especially  is  it  necessary  to  take  care  with  the  inner 
end,  which  on  being  led  out  crosses  the  other  coil-layers,  and 
must  be  insulated  therefrom  by  strips  of  mica.  Heavy  cables  have 
to  be  joined  to  the  terminal  ends  of  the  coils,  and  the  joint  between 
these  and  the  strip  must  be  most  carefully  insulated. 

Example  4. — Traction  Motor  Field  Coils — Ordinary  Con- 
struction.—The  coil  is  wound  from  wire  of  the  required  size,  and 
each  layer  is  painted  with  a  good  enamel  or  varnish.  The  corners  and 
the  places  where  wires  cross  over  are  protected  by  asbestos  -f$  inch 
thick.  Where  special  protection  is  necessary,  as  at  the  first  and  last 
turns  of  the  first  layer  of  wire,  a  turn  of  string  or  rope  may  be  wound 
parallel  with  the  wire,  so  that  any  pressure  comes  on  this  and  not  on 
the  wire  itself.  The  same  protection  may  be  adopted  in  the  last 
layer  where  the  coil  comes  against  the  yoke.  The  coil  should  then 
be  baked  in  an  oven  for  twelve  hours,  or  if  a  vacuum  oven  is  available 
half  this  time  will  be  sufficient.  While  still  hot  it  should  be  plunged 
into  insulating  varnish  and  afterwards  dried  in  a  stove  for  ten  hours, 
or  in  a  vacuum  oven  for  five  hours,  at  a  temperature  of  about  1 00°  C. 
Inside  the  coil,  and  surrounding  the  pole,  should  be  placed  a  liner  of 
fullerboard  ^  inch  thick,  which  has  been  previously  treated  with 
varnish  and  well  dried  to  render  it  non-absorbent,  and  at  either  end 
there  should  be  a  washer  of  fullerboard  or  press-spahn  TT6  inch  thick. 
The  coil  may  finally  be  taped  all  over  and  again  treated  with  varnish, 
the  usual  care  being  exercised  in  the  manner  of  bringing  out  the 
terminals. 


INSULATION 


'43 


Space-factor  of  Armature  Slots. — In  this  case  also  the  value 
of  the  space-factor  will  depend  upon  a  number  of  conditions,  the 
chief  of  which  are  :— 

(a)  Type  of  winding  and  method  of  insulation. 

(b)  Shape  of  wire  section,  whether  rectangular  or  round. 

(c)  Number  of  armature  coils  corresponding  to  one  slot. 

(d)  Voltage  and  speed. 

(a)  Type  of  Winding. — We  have  assumed  the  winding  to  be 
always  of  the  drum-type,  with  cylinder  end  connections  and  former- 
wound  coils.  The  coils  corresponding  to  one  slot,  separated  by  insu- 
lating strips,  are  usually  bound  together  by  wrapping  with  tape 
10  mils  thick,  as  mentioned  and  illustrated  on  p.  114.  These  units 
are  then  always  dried  in  an  oven  (as  described  for  field  coils),  im- 
pregnated with  a  good  varnish,  and  dried  again.  Often  this  is 
repeated,  and  in  some  cases  it  is  carried  out  three  times.  These 
units  are  then  placed  in  the  slots.  Sometimes  an  insulating  compo- 
site liner  is  placed  in  the  slot,  and  sometimes  this  protection  is  put 
inside  the  taping  and  so  forms  part  of  the  coil.  In  any  case  the 
insulation  thickness  between  wire  and  core  is  rarely  less  than 

35  mils  for  100  volt  machines  (1500  K.M.S.  volts  flash-test) 
40        „       200  „  (2000  volts  flash-test) 

60        „       500  „  (3000       „         „         ) 

Fig.  86  shows  some  examples  of  slot  coil- windings,  in  which  the 
distinction  between  the  slot-lining  and  the  taping,  etc.,  round  the 


/  234 

FIG.  86. — ARRANGEMENT  OF  WIRE  AND  FORMER  WINDINGS  IN  SLOT. 

coils  is  brought  out.     Table  IX.  gives  some  typical  examples  of  com- 
posite slot-linings  for  various  voltages. 


144    CONTINUOUS   CURRENT   MACHINE   DESIGN 


TABLE  IX. 
SLOT  LININGS  FOR  TAPED  FORMER-WOUND  COILS. 


Volts  of 
machine. 

Press-spahn  or 
fuller-board, 
mils. 

Oiled  cloth  or 
paper, 
mils. 

Mica  or  mica 
compound. 

Press-spahn  or 
fuller-board. 

Insulation 
thickness. 

Up  to  150 

„    250 
„    600 

10 
10 
12 

5 
10 
12 

14 

10 
10 
12 

2  x  25 
2  X  30 
2  x  50 

Between  the  groups  of  coils  themselves,  or  between  the  upper 
layer  and  lower  layer  of  the  end  connections,  varnished  press- 
spahn  20-30  mils  thick  may  be  used. 


< —      7  mils  fuller-board. 


24  mils  tape. 

4  papers  =  12  mils. 
10  mils  tape. 

|-in.  wood. 
No.lSS.W.G.D.C.C. 


pIG.  87. — SECTION  THROUGH  SLOT  OF  A  TRACTION  MOTOR. 

Not  infrequently  in  modern  motors  the  slot-lining  is  partly  or 
wholly  omitted.  In  such  cases,  of  course,  the  coils  themselves  must 
be  more  heavily  insulated,  and  Fig.  87  illustrates  such  an  arrange- 
ment suitable  for  a  500-volt  traction  motor  for  tramway  work.  An 
armature  so  wound,  if  properly  baked  and  impregnated,  would  with- 
stand a  test  of  3000  volts  for  three  minutes. 

Another  example  of  slot  insulation  in  which  no  slot  liner  at  all 
is  used  is  as  follows  : — 

The  individual  coils,  instead  of  being  separately  taped,  as  in 
Fig.  87,  are  separated  by  shellaced  press-spahn  10  mils  thick. 

The  coils  corresponding  to  one  slot  are  bound  together  by  taping, 


INSULATION 


as  in  Fig.  87,  up  to  a  thickness  of  20  mils,  and  the  two  half 
coils  in  the  same  slot  are  separated  by  a  strip  of  press-spahn 
10  mils  thick.  This  arrangement  is  for  220  volts. 

(b)  Shape  of  Wire. — The  effect  of  the  shape  of  the  wire  upon  the 
space-factor  of  the  slot  is  well  illustrated  in  Fig.  88,  giving  the 
comparison  between  the  slot  dimensions 
for  coils  of  the  same  copper  area  and 
of  the  same  insulation,  for  round  and 
rectangular  conductors  respectively. 
The  saving  obtained  by  using  rect- 
angular wire  amounts  to  a  difference 
in  space-factor  of  from  15  to  25  per 
cent.,  20  per  cent,  being  a  fair  average. 
A  very  convenient  winding  may  be 
made  from  a  thin  flat  strip  wound  with 
the  flat  side  parallel  to  the  bottom  of 
the  slot.  This  arrangement  is  adopted 
in  Adamson's  crane-motors.  Generally 
speaking,  rectangular  wires  are  more  FlG-  88-  —  SPACE  -  FACTORS  OP 
difficult  to  wind  than  round  wires.  5S55J-*  KECTANGULAB  GoN" 

Bar  Windings. — When  the  copper 

conductor  is  too  large  in  section  to  admit  of  coil- winding,  each  turn 
is  individually  made  on  a  former,  and  the  armature  is  said  to  be 


FIG.  89. — ARRANGEMENT  OP  BAR  WINDINGS  IN  SLOT. 


bar-wound.  In  these  cases  there  are  usually  as  many  commutator- 
sections  as  armature-turns.  Sections  through  slots  so  filled  are 
shown  in  Fig.  89,  and  Table  X.  gives  the  usual  slot-lining  for 
various  voltages. 


146     CONTINUOUS   CURRENT   MACHINE   DESIGN 


TABLE  X. 


Volts  of 
machine. 

Press-spahn  or 
fuller-board, 
mils. 

Oiled  cloth  or 
paper, 
mils. 

Mica  or 
micanite. 

Press-spahn  or 
fuller-board. 

Total 
insulation. 

Up  to  150 

10 

5 

_ 

10 

2  x  25 

„    200 

10 

12 

— 

12 

2  x  34 

„    600 

10 

15 

18 

10 

2  x  53 

(c)  and  (d)  Number  of  Armature- Coils  per  Slot,  Voltage  and 
Speed. — Each  armature  for  a  given  voltage  and  speed  has  a  number  of 
coils  which  is  fairly  definitely  fixed.  The  number  of  slots  to  be 
used,  however,  for  each  armature,  admits  of  some  choice;  and  in 
consequence  the  number  of  coils  per  slot  is  a  matter  for  attention. 
Apart  from  the  limitations  referred  to  on  p.  114,  the  number  of  coils 
per  slot  should  be  as  large  as  is  consistent  with  reasonable  slot- 
dimensions  ;  for  the  fewer  the  slots  the  better,  as  a  rule,  is  the 
utilization  of  space. 

On  the  other  hand,  the  larger  the  number  of  turns  per  coil  the 
worse  is  the  space-factor,  because  the  greater  is  the  number  of 
conductors  per  slot,  and  each  conductor  must  be  insulated.  Thus 
the  difference  between  four  and  two  coils  per  slot  corresponds  to  an 
increase  in  space-factor  of  about  12  per  cent.,  i.e.  a  change  from  0'4 
to  0*45  about.  On  the  other  hand,  doubling  the  number  of  turns  per 
coil  decreases  the  space-factor  usually  from  5  to  10  per  cent.,  accord- 
ing to  the  size  of  wire  involved. 

General  Values  of  Slot  Space-factor. — Paying  due  regard  to 
the  above  points,  the  following  table  gives  average  values  of  the 
space-factor  for  various  outputs  and  voltages,  with  their  corresponding 
testing  pressure  in  R.M.S.  volts  (5  minutes'  application) : — 


TABLE  XI. 
MACHINE  VOLTAGE  UP  TO  150;  TESTING  VOLTAGE  2000. 


K.W.  output 

5 

10 

15 

20 

30 

40 

50 

60 

80 

100 

200 

Space-factor 

0-28 

0-34 

0-38 

0-4 

0-43 

0-45 

0-47 

0-48 

0-5 

0-51 

0-52 

INSULATION 
TABLE  XII. 


'47 


MACHINE  VOLTAGE  UP  TO  250  VOLTS;  TESTING  VOLTAGE  UP  TO 

2500  VOLTS. 


K.W.  output 

5 

10 

15 

20 

30 

40 

50 

60 

80 

100 

200 

Space-factor 

0-24 

0-28 

033 

0-34 

0-37 

0-4 

0-41 

0-42 

0-43 

0-43 

0-44 

TABLE  XIII. 

MACHINE  VOLTAGE  UP  TO  600  VOLTS;  TESTING  VOLTAGE  UP  TO 

3500  VOLTS. 


K.W.  output 

5 

10 

15 

20 

30 

40 

50 

60 

80 

100 

200 

Space-factor 

0-2 

0-24 

0-26 

0-29 

0-32 

0-34 

0-34 

0-35 

0-36 

0-37 

0-38 

Insulation  between  Armature  Laminae. — This  may  be  carried 
out  (a)  by  pasting  thin  paper  on  to  one  side  of  each  disc ;  (b)  by 
Japanning  or  varnishing  the  discs ;  (c)  by  treating  the  discs  with 
special  preparations,  such  as  "Insuline."  The  armature  discs  are 
usually  stamped  from  metal  about  18  to  20  mils  thick,  and  the  space 
occupied  by  the  insulation  is  for  method  (a)  about  12  per  cent.,  for 
methods  (I)  and  (c)  about  8  to  10  per  cent.  The  use  of  paper  un- 
doubtedly results  in  the  least  eddy  currents ;  but  the  other  methods 
are  good  enough,  especially  if  a  sheet  of  paper  be  used  about  every 
twenty  stampings. 

Insulation  of  Brush-Gear  parts,  Terminal  Blocks,  etc. — For 
such  purposes  as  these,  mechanical  strength  and  small  surface-leakage 
are  of  great  importance.  Consequently  moulded  blocks  of  various 
special  compounds,  such  as  ambroin,  isolite,  micanite,  etc.,  have 
replaced  the  older  materials  like  ebonite,  vulcanized  fibre  and  wood. 
Very  many  beautifully  moulded  and  very  convenient  special  insulators 
are  on  the  market  for  these  purposes.  Porcelain  is  used  in  some 
special  cases.  For  particulars  of  dimensions,  etc.,  the  reader  is 
referred  to  the  various  makers'  catalogues. 

Commutator  Insulation. — This  may  be  divided  into  three  parts, 
viz. — 

1.  That  which  insulates  the  sections  from  the  clamping  rings. 

2.  That  which  lies  between  the  sections  and  the  shaft. 

3.  That  which  insulates  a  section  from  its  neighbours. 


148     CONTINUOUS   CURRENT   MACHINE   DESIGN 

For  the  first  and  the  third  purposes,  except  in  the  special  case  of 
very  low  voltage  machines,  mica  or  micanite  is  always  used.  The 
end-rings  for  the  former  purpose  are  specially  moulded  to  the  correct 
form  by  micanite  makers ;  but  for  the  latter  work  it  is  usual  to  buy 
mica  plates  and  split  them  to  suit  the  thickness  of  insulation  required, 
fixing  them  together  by  means  of  as  little  shellac  varnish  as  possible. 

For  protecting  the  inside  of  the  sections  and  separating  them 
from  the  shaft,  sometimes  micanite,  more  often  press-spahn,  is 
adopted :  for  the  only  object  of  this  liner  is  to  protect  the  sections 
from  short-circuit  by  the  possible  accumulation  of  dust,  or  by  any 
little  bits  of  metal  left  accidentally  when  putting  the  machine 
together.  Figs.  Ill  and  112  give  an  idea  of  the  usual  construction ; 
and  the  thicknesses  of  insulation  employed  are  given  below  with  their 
corresponding  voltages. 

THICKNESS  OF  MICA  BETWEEN  SEGMENTS. 

Machine  voltage.  Thickness  in  mils. 

Up  to  250 25 

„     600 .        .        .        .         .     25  to  35 

The  mica  selected  should  be  such  as  will  wear  at  the  same  rate  as 
the  copper  segments.  The  best  Indian  mica  is  probably  as  good  as 
any  for  this  purpose,  and  the  author  prefers  it  when  of  a  greenish 
shade  with  or  without  greenish  spots. 

The  micanite  end-rings  vary  from  40  to  100  mils  in  thickness, 
according  to  the  size  of  the  machine ;  an  average  value  is  A-  in. 
(=  62-5  mils). 

Other  details  of  insulation  will  be  best  studied  from  examples 
given  in  Chap.  XI.,  and  under  the  various  machines  worked  out. 


CHAPTER  XI 


s  Rivets. 


GENERAL  MECHANICAL  CONSTRUCTION 

IN  the  preceding  chapters,  the  considerations  which  govern  and  limit 
the  proportions  of  the  individual  parts  of  continuous-current  machines 
have  been  dealt  with  in  some  detail.  It  is  now  necessary  to  empha- 
size a  few  important  points  in  the  relative  arrangement  and  con- 
struction of  these  parts ;  and  since  details  of  mechanical  construction 
are  largely  in  the  discretion  of  the  designer,  where  no  theoretical  laws 
as  to  strength  apply,  dimensioned  examples  will  be  given  to  form  a 
safe  guide. 

I.  Field-Magnets. — It  has  already  been  shown  (pp.  5-7)  that  the 
general  mechanical  construction  of  the  field-magnet  influences  to  no 
small  extent  the  subsequent  design 
calculations.  For  this  reason,  questions 
relating  to  the  shape  and  fixing  of  the 
poles,  to  the  form  of  the  shoes  and  to 
the  yoke  material  and  shape  have 
already  been  dealt  with.  Other  details 
of  field  design  will  be  found  in  sub- 
sequent examples,  as,  for  instance,  on 
pp.  208,  218.  Where  poles  and  shoes 
are  made  up  of  stampings,  it  is  usual 
to  bind  the  latter  together  by  means  of  . 
rivets,  as  shown  in  the  small  pole-  FlG>  90-p°^^cE  LAMINA- 
stamping.  Fig.  90,  and  in  the  completed 

pole,  Fig.  91.  These  groups  are  then  held  in  position  by  set-screws 
passing  through  the  yoke  and  into  the  tapped  stampings,  as  in 
Fig.  91 ;  or  into  a  rectangular  or  round  wrought-iron  nut  pressed 
into  a  hole  left  in  the  stampings,  as  indicated  in  Fig.  90. 

The  two  outermost  of  each  group  of  stampings  are  usually  of 
thicker  material,  so  as  to  form  supports  for  the  entire  group,  as  well 
as  providing  thickness  for  the  countersunk  rivet-heads  (Fig.  91). 

An  illustration  of  the  construction  of  a  field  magnet  with  solid 


i5o     CONTINUOUS   CURRENT   MACHINE   DESIGN 

steel  poles  and  laminated  shoes  is  shown  in  Fig.  92,  which  gives 
details  of  a  machine  designed  by  the  author. 


LAMINATED 
\    POLE  PIECE. 


y  Iron  Rivets, 
CountersunK   Heads. 


LAMINATIONS. 


FIG.  91. 


—         i —   — 
FIG.  93. — DETAIL  SKETCH  OF  VENTILATED  FIELD-COIL  (CEAMP). 

Fixing  of  Field  Coils. — This  depends  entirely  upon  the  construc- 
tion and  insulation  of  the  coils,  as  illustrated,  for  instance,  in  Figs.  41, 


FIG.  85. — TAPED  FIELD-COIL. 


FIG.    97. — MACHINE     WITH     END-PLATE    AND 

YOKE   CAST    TOGETHER    (GENERAL    ELECTRIC 

COMPANY). 


— ISO  K.W  TRACTION  GENERATOR— 


FIG.  92. — GENERAL  ARRANGEMENT  OF  FIELD-MAGNET  (CRAMP). 

[To  face  p.  150. 


GENERAL   MECHANICAL   CONSTRUCTION        151 

42,  43,  45,  and  85.  The  support  for  the  coil  is  usually  provided  by  the 
shoe,  projections  or  brackets  being  fixed  thereto,  upon  which,  when  pro- 
tected by  insulation,  the  coil  rests.  To  prevent  movement  when  in 
place,  insulating  wedges,  often  of  wood,  are  used  between  the  coil  and 
pole ;  or  a  method  of  fixing  like  that  illustrated  in  Fig.  92  may  be 
adopted.  A  detail  of  this  coil  is  given  in  Fig.  93,  and  it  will  be 
noticed  that  the  series-coil  is  spaced  apart  from  the  shunt-winding, 
the  supporting  bolts  passing  through  wooden  sector  separators. 

Fixing  of  Interpoles. — Fig.  94  shows  the  ordinary  method  *  of 
fixing  interpoles  as  arranged  by  Lawrence  Scott  &  Co.  In  order  to 
find  room  for  the  interpole  coil,  sometimes  either  the  main  windings 
or  the  interpole- winding  has  to  be  specially  shaped.  In  any  case  it 
is  advantageous,  when  the  main  poles  are  circular,  to  displace  the 


Cora. 


FIG.  94.  INTEEPOLE  AND  MAIN  POLE       FIG.  95.— PHOENIX  PATENT  INTERPOLE. 
(LAWRENCE  SCOTT). 

interpole  with  respect  to  the  main  pole,  as  shown  in  the  plan,  Fig.  95. 
It  is  also  seen  from  this  drawing  that  the  interpole-shoe  need  not  be 
of  the  same  axial  length  as  the  armature.  It  is,  of  course,  an 
advantage  to  have  it  shorter,  as  the  leakage  is  thereby  reduced,  and 
this  idea  formed  one  of  the  main  points  in  the  original  Pohl  patent, 
which  is  now  maintained  by  practically  all  the  leading  firms.  To 
reduce  the  leakage  still  further,  the  Phoenix  Dynamo  Co.  have 
patented  the  arrangement  of  cutting  away  that  pole-shoe  to  which 
most  leakage  would  take  place,  as  shown  in  Fig.  95. 

Machining  of  Field-magnets.— Field-magnets  should  be  so 
designed  as  to  reduce  the  machining  to  the  lowest  possible  limit.  To 
compass  this  end  it  is  desirable  to  arrange  so  that  as  many  surfaces 
as  possible  may  be  machined  at  one  setting,  due  regard  being  paid  to 
the  tools  available.  Thus,  where  the  poles  are  separate  from  the 

*  Cf.  Journal  Instf.  E.E.,  vol.  39,  no.  186,  p.  593. 


152     CONTINUOUS   CURRENT   MACHINE   DESIGN 


yoke,  the  seatings  for  these  poles  may  be  bored  or  they  may  be 
planed;   and  though  the  former  is  cheaper,  it  often  necessitates  a 

large  boring  machine.  Where 
the  pole-seats  are  bored  and 
the  poles  are  made  up  of 
stampings,  some  makers  do 
not  machine  the  actual  arma- 
ture bore,  as  stampings  can 
be  bought  sufficiently  accu- 
rately finished  to  render  this 
unnecessary.  A  double  gain 
results,  in  the  absence  of 
machining,  and  the  reduction 
of  eddy  currents.  At  the 
Q  same  setting,  and  often  with 
the  same  tool,  the  pole- seat- 
ings (or  the  pole-faces),  and 
the  seatings  for  the  bearings, 
H  may  be  machined.  This  ne- 
cessitates cylindrical  seatings 
for  the  bearing  -  standards  ; 
and  if  the  latter  be  turned 
up  with  the  bearing-bush  as 
pp  centre,  absolute  alignment  of 
bearings,  shaft,  and  armature 
bore  is  easily  obtained.  Of 
course  this  construction  can 
only  be  applied  in  machines 
of  moderate  size.  In  Fig.  96, 
which  refers  to  medium -speed 
direct  -  coupled  generators  as 
recommended  by  the  American 
Standards  Committee,  flat 
standard  seatings  are  adopted. 
A  careful  examination  of 
machines  of  well  -  known 
makers  will  show  better  than 
any  description  the  various 
methods  of  simplifying  the 
machining,  which  must  be 
borne  in  mind  when  getting 
out  a  new  design. 

End -plates    and    Bear- 
ings.— In  small  machines,  the 
bearings   (usually   of  the  ring-lubricated   type,  though   sometimes 


GENERAL   MECHANICAL   CONSTRUCTION        153 


b   i 


U)  _ 

§    2 


S 


& 

O 

§ 


CO 

§ 


ing-d 
bolts. 


ft       •>        «.S 


GO  ^  O  0  <M  -rH  CO 
O  tD  C^  00  Ci 


o  <g  S  *o  oT 


pace  occupied 
on  shaft 
between  the 
limit  lines. 


Diameter  of  engine 
at  armature  fit. 


I!,- 

° 


CO  O  00  i—  i  •<*  !>•  (M 
(M  (M  <M  CO  CO  CO  ^ 


»o  ic  to  co  «o  co  co 


»O  GO  i—  i  !>•  <M  >O  GO 
(M  <N  CO  CO 


co  co  co  -^  •<*  o 


to  to  to  10  to  lo 

•  HiH§H§H§^ 

JH   H   Ir-    H   IH    ;H 


^  »O  O  C^  CO  O  1-1 


il 


"^  -rt*  ^  iO  0  t-  CO 


•^  O  0  t^  CO  O  1-* 


O  t-  CO 


o  o  o  »o  o  »o 

T—  i  O  O  l>  <^>  <M 

CO  CO  (N  CO  C^  (M 


»O  iO  O  iO  O  O  O 
CM  CO  O  t>  O  iO  O 


I}: 

•s-s-i 


_ 


111 

s«g 

&Ij 


154     CONTINUOUS   CURRENT   MACHINE    DESIGN 

ball-bearings  (Fig.  124)  or  wick  lubricators  are  adopted)  form  part  of 
the  end  plate,  and  are  carried  by  the  yoke.  This  construction  gives 
excellent  alignment,  is  cheap,  and  gives  protection  to  the  whole 
machine.  One  end-plate  may  be  cast  with  the  yoke,  as  in  Fig.  97  ; 
this  arrangement  has  the  advantage  of  cheapness,  but  also  the  dis- 
advantage that  it  is  only  possible  to  withdraw  the  armature  at  one 
end,  unless  the  frame  be  split.  The  bearing  in  relation  to  its  loose 
end-plate  may  be  arranged  as  in  Fig.  98  or  as  Fig.  99.  In  the  latter, 
E  is  merely  a  screw  to  which  the  cap-chains  may  be  attached. 

In  larger  machines  the  bearings,  also  of  the  ring-lubricated  type, 
are  more  usually  carried  by  the  bedplate,  as  is  sufficiently  illustrated 


•JOKW  MOTOR.— 

250  V01.T5.  70ORPH.  

GENERAL  ARRANGEMENTS 


FlG.    98. 


in  Figs.  96  and  100.  The  number  of  lubricating  rings  is  generally 
two,  but  bearings  less  than  6  inches  long  sometimes  have  but  one. 
The  bearing-bush  itself  is  sometimes  rigidly  fixed  in  its  shell,  but 
more  often  it  is  arranged  so  that  it  can  swivel  slightly,  as  in  Figs.  98 
and  99.  In  small  machines  it  is  constructed  of  hard  brass,  or  of 
gun- metal,  or  even  of  phosphor-bronze.  In  large  machines  it  is  con- 
structed of  cast  iron  and  lined  with  white  metal.  Typical  cases  of 
the  former  are  seen  in  Figs.  98  and  99,  while  Fig.  101  shows  an 
arrangement  of  the  latter  class. 

Proportions  of  Journals  and  of  Bearings. — From  the  examples 
already  given,  and  from  the  shaft  calculations  given  later,  the  pro- 
portions of  dynamo  journals  can  be  ascertained.  The  strengths 


GENERAL   MECHANICAL   CONSTRUCTION       155 


allowed,  as  well  as  the  bearing  surfaces,  are  usually  far  in  excess  of 

those  prescribed   by   pure   theory,   and  are    more    generous    than 

mechanical    engineers    use    under      -,  ,  , 

similar    circumstances    for    other  -»j-»—  -47&- *j^ 

machinery.     Keasons  for  this  are 

to  be  found  in  the  importance  of 

keeping  the  armature  central;  in 

the  constant  running  required ;  in 

the  relatively  high  speed  and  large 

weight  of  the  armature;    in   the 

liability   to    sudden    strain    if    a 


FIG.  99. — DETAIL  OF  MOTOR-BEARING 
(JONES). 


FIG.  100. — DETAIL  OF  DYNAMO- 
BEARING  (  JONES). 


short  circuit  occur ;  in  the  small  attention  given  and  the  absolute 
necessity  for  freedom  from  breakdown.      The  ratio,  journal-length 


156     CONTINUOUS   CURRENT   MACHINE   DESIGN 

to  journal-diameter  varies  widely ;  but  on  an  average  may  be  taken 
at  3  to  3J. 


I 


FIG.  101. — SECTION  THROUGH  PABT  OP  FIG.  100. 

Shafts. — Dynamo  shafts  are  always  made  largest  in  the  middle, 
stepped  down  to  accommodate  the  commutator  bush,  and  again  at 
the  journals  (see  Fig.  98).  Oil-throwers  are  provided  at  the  inner 
end  of  each  journal,  and  shoulders  to  limit  the  end  movement.  The 
diameter  of  the  shaft  at  the  journals  is  sometimes  calculated  from  a 
formula  of  the  type — 

Diameter  of  shaft  =  constant  %/  H.P.  ~  revs,  per  minute  * 

in  which  the  constant  depends  upon  the  material  used,  and  for  steel 
is  usually  taken  as  7.  Such  calculations  are  not  very  satisfactory,  as 
they  are  based  upon  torsional  forces  only,  the  constant  being  taken 
large  enough  to  cover  any  possible  bending.  The  pure  twisting 
moment  on  the  shaft  may  be  calculated  from  the  usual  expression- 
Twisting  moment  in  inch-pounds  =  63,000  H.P.  4-  revs,  per  minute 

Bending  Moment. — Some  designers  consider  only  the  bending 
moment  due  to  armature  and  commutator.  They  assume  that  the 
weight  is  concentrated  at  the  centre,  and  that  the  shaft  acts  as  a 
beam  supported  at  the  bearing  centre  at  either  end.  The  shaft  is 
then  designed  so  that  the  deflection  due  to  this  load  is  less  than 

*  Cf.  "  Unwin's  Machine  Design,"  13th  Ed.,  vol.  i.  p.  214. 


GENERAL   MECHANICAL   CONSTRUCTION       157 

3    per  cent,  of   the  air-gap  length.     Thus,  according   to  the  usual 
formula  for  beams  — 

Deflection  at  centre  in  inches  =  —  '-  -  **/  ,  .     —  ^r-- 

3-rra  .  (diameter)4 

The  weight  in  this  formula  is  that  of  armature  and  commutator 
in  tons  ;  the  length  is  the  distance  from  bearing  centre  to  bearing 
centre  in  inches;  and  the  diameter  is  that  of  the  shaft  centre  in 
inches,  a  is  the  modulus  of  elasticity,  usually  taken  at  about  12,000 
for  steel  shafts. 

This  method  gives  reliable  results,  although  it  does  not  take  into 
account  all  the  factors,  or  even  all  the  bending  forces.  For  instance, 
if  there  is  a  deflection  the  armature  will  be  out  of  centre,  and  a 
magnetic  pull  will  result.  This  can  be  approximately  calculated, 
but  the  extra  deflection  due  to  it  is  usually  far  less  than  the  reduc- 
tion of  deflection  due  to  the  stiffness  given  by  the  armature-spider 
and  commutator-sleeve  ;  also,  since  the  load  has  been  considered  as 
concentrated  when  it  is  really  distributed,  a  further  factor  of  safety 
is  added.  In  any  case,  to  reduce  the  shaft  to  the  smallest  theoretical 
diameter  would  be  a  very  short-sighted  policy. 

Combined  Bending  and  Twisting.  —  If  by  an  approximation 
like  that  in  the  previous  paragraph  the  bending  moment  can  be 
calculated,  it  is  usually  found  that  the  twisting  moment  is  negligible 
beside  it.  When  this  is  not  the  case,  the  equivalent  twisting  moment 
can  be  found  from  the  usual  expression  *  — 

TX  =  ,B-f 


in  which  Tl  =  resultant  or  equivalent  twisting  moment  in  inch-lbs., 
B  =  bending  moment, 
T   =  pure  twisting  moment  as  calculated  on  p.  156. 

Whence,  a  formula  similar  to  that  on  p.  156  may  be  obtained,  giving  : 
diameter  of  shaft  =  constant  <J/Ti,  and  the  constant  corresponding 
to  the  value  7  in  the  previous  equation  is  0*175.  The  value  of  B  in 
inch-lbs.  is  often  taken  as  weight  of  armature  and  commutator 
multiplied  by  J  of  the  length  between  bearing  centres.! 

It  should  be  remembered  that  there  is  a  critical  speed  for  all 
shafts  at  which  "  whipping  "  is  set  up.  This,  however,  rarely  occurs 
at  less  than  2000  revs,  per  minute,  and  consequently  is  of  importance 
for  very  high-speed  machines  only.  It  is  not  within  the  scope  of  the 
present  work. 

In  the  absence  of  practical  experience,  the  reader  is  advised  to 
calculate  his  shaft  as  carefully  as  possible  from  the  formulae  given, 
and  then  to  compare  his  results  with  such  examples  as  those  in 
Table  XV. 

*  "  Unwin's  Machine  Design,"  13th  Ed.,  vol.  i.  p.  215. 

t  Goodman,  "  Mechanics  applied  to  Engineering,"  p.  364  and  Chap.  XIV. 


158     CONTINUOUS   CURRENT   MACHINE   DESIGN 

TABLE  XV. 


Kilowatts. 

Revolutions  per 
minute. 

Journal  diameter  in 
inches  (pulley  end). 

4 

1000 

ii" 

5 

1000 

i|" 

5 

600 

if" 

10 

1000 

Mr 

14 

850 

2J" 

20 

600 

3" 

60 

500 

4- 

100 

200 

5* 

250 

125 

6" 

FIG.  102. — TRACTION  MOTOR  ARMATURE  Disc. 


FIG.  104. — ARMATURE-CORE,  END-PLATES  AND  VENTILATING  DUCTS 
(VERITY'S,  LTD.). 


FIG.  107. -ARMATURE-CORE  AND  SPIDER  (BRITISH  WESTINGHOUSE  Co.). 

[To  face  p.  158. 


GENERAL   MECHANICAL   CONSTRUCTION       159 

The  various  steps  and  collars  on  the  shaft  of  a  small  machine  are 
seen  in  Fig.  98. 

Armature  Construction.  —  In  very  small  machines  the  stamp- 
ings of  which  the  armature  is  composed  are  threaded  straight  on 
the  shaft  and  clamped  in  position  by  suitable  end  plates  (Fig.  98). 
Wherever  possible,  however,  the  stampings  are  threaded  upon  a 
4-,  6-,  or  8-armed  "  spider,"  whereby  ample  ventilation  to  core  and 
windings  may  be  secured.  In  machines  with  armatures  of  about 
12  inches  diameter  there  is  hardly  room  for  a  spider,  but  there  is 
room  for  more  iron  than  is  necessary.  In  these  cases  ventilation 
holes  are  made  in  the  stampings,  as  illustrated  in  Fig.  102,  for  a 


SECTIONAL 


END     ELEVATION 


FIG.  103. — END-PLATE  OR  "CORE-HEAD 


traction  motor  disc ;  examples  of  end-plates  and  the  thick  end  sup- 
porting stampings  of  such  armatures  are  shown  in  Fig.  129,  p.  215, 
and  again  in  Figs.  103  and  104.  An  armature  of  medium  size 
mounted  upon  a  spider  is  shown  in  Figs.  105  and  106,  and  a  method 
of  arranging  still  larger  armatures  is  given  in  Fig.  107.  In  all  cases 
the  ventilating  spaces  are  clearly  shown.  In  Fig.  98  the  passages 
through  the  core  are  dotted  and  marked  with  the  letter  C. 


160     CONTINUOUS   CURRENT   MACHINE   DESIGN 


:  ' 

\ 

~  T  

J 

| 

GENERAL    MECHANICAL   CONSTRUCTION        161 

To  drive  the  discs  keys  or  feathers  are  used.  In  Fig.  98  the  long 
feather  is  clearly  shown ;  and  in  Fig.  105,  there  are  two  keys,  one 
on  the  end  of  a  spider  arm  to  drive  the  discs,  and  another  in  the 
shaft  to  drive  the  spider. 

Radial  Ventilation  through  Armature.— The  stampings  of 
which  the  armature  is  composed  are  separated  about  every  three 
inches  to  allow  of  the  passage  of  air,  as  is  shown  in  the  illustrations. 
These  passages  or  "  ducts  "  are  arranged  by  means  of  radial  projections 
affixed  to  a  stamping,  or  by  a  light  ribbed  cast  plate  riveted  to  the 
stamping  next  to  the  duct  (Fig.  108).  The  projections  in  the  latter 


FIG.  108.— DISTANCE-PIECE  (BRITISH  THOMSON- HOUSTON  Co.). 

case  reach  right  to  the  end  of  the  teeth,  and  the  ducts  are  from 
i  in.  to  f  in.  wide.  , 

Strength  of  Spider  Spokes. — For  a  steady  load  it  is  easy  to 
calculate  the  section  of  the  spider  arm.  For  the  arm  or  spoke  may 
be  considered  as  a  beam  loaded  at  its  outer  end  with  a  weight  equal 
to  its  share  of  the  pull  at  the  armature  periphery.  The  total  value 
of  the  latter  is  evidently 

HP.  6600 
irDn 

Let  the  radial  distance  from  the  smallest  section  of  the  arm  to  the 
armature  surface  be  llt  and  let  the  section  of  the  arm  be  rectangular. 
Then,  if  the  number  of  spokes  be  ns— 

H.P.  x  6600,  &!  x  V 

/x  =  safe  stress  X pr— — 

ns  6 


where  ^  =  smallest  width  of  spoke  parallel  to  shaft 

=  length  of  armature,  practically  =  L  inches, 
A!  =  thickness  of  spoke  at  its  smallest  section  at  right  angles 

to  the  shaft  in  inches, 
and       n  =  revolutions  per  second. 


M 


1 62     CONTINUOUS   CURRENT   MACHINE   DESIGN 

For  cast  iron,  allowing  a  factor  of  safety,  the  safe  stress  may  be  about 
1000  Ibs.  per  sq.  inch,  whence 


On  account  of  the  fact  that  the  pull  is  exerted  under  the  pole- 
faces  chiefly,  and  not  uniformly  around  the  armature,  and  also 
because  of  possible  sudden  strains,  the  value  of  hi  is  usually  con- 
siderably greater  than  that  given  by  this  formula,  as  is  clearly  seen 
in  the  illustrations. 

I 


FIG.  109. — END  CONNECTIONS. 

Armature  End  Connections. — In  the  cylinder- wound  or 
"  barrel- wound  "  armature,  which  is  now  almost  universal,  the  arma- 
ture coils  project  from  the  armature  at  either  end,  and  there  lie  along 
the  surface  of  a  cylinder  concentric  with  the  armature.  Usually,  for 
various  reasons,  this  cylinder  is  slightly  conical,  as  is  seen  in  the 
several  illustrations.  Part  of  the  surface  is  developed  in  Fig.  109, 
and  the  construction  there  shown  determines  the  length,  "  Lc,"  that 
the  end-connections  must  project,  and  therefore  also  the  length  of 
the  end-support.  If  Ws  be  the  width  of  a  slot,  Wt  the  width  of  a 
tooth,  then  it  is  seen  that — 


cos  a  = 


whence  Le  is  determined  if  S  be  known. 


GENERAL   MECHANICAL   CONSTRUCTION       163 

Now,  S  is  half  the  number  of  slot-pitches  spanned  by  one  coil 
plus  I  a  slot-pitch  (nearly),  and  this  is  known  from  the  winding 
scheme. 

The  total  amount  that  the  end  windings  project,  is  Le  plus  an 
allowance  at  either  end,  as  shown  in  the  sketch,  and  usually  Le  -{-  £ " 
is  a  sufficient  total  length. 

Example. — Assume  that  the  armature  winding  calculated  on 
p.  114  lies  on  an  armature  13  inches  diameter  with  slots  1*4  inch 
deep  and  0'5  inch  wide ;  then  the  slot  pitch  at  the  bottom  of  the 
slots  is  0'78  inch.  The  slot  winding-pitch  from  p.  114  is  10  slots 
=  7*8  inches. 

/.  S  =  3-9"  +  0-39"  =  4-3"  nearly 

Thus  Le  =  S    ,_    °'5"   =  =  4-3:^3  =  3-6" 
x/(078)2  -  0-25  0-598 

Le  +  I"  =  4-35" 

Fixing  of  Armature  Coils. — Modern  armatures,  being  pro- 
vided with  slots  in  which  the  armature  coils  lie,  have  this  advan- 
tage over  the  older  smooth-core  machines — that  the  pull  between  the 
armature  and  the  magnetic  field  falls  on  the  armature  teeth  instead 
of  upon  the  conductors  themselves.  There  is  in  consequence  only 
one  force  practically  to  reckon  with  in  fixing  the  armature  coils,  viz. 
centrifugal  force. 

The  methods  in  use  to  guard  against  movement  of  the  coils  are 
two,  viz.  wooden  wedges  fixed  in  the  slots,  with  binding  wires  over 
the  end  connections ;  or  binding  wires  only. 

When  the  first  method  is  adopted  the  teeth  are  specially  shaped 
to  accommodate  the  strips  of  wood,  as  shown  in  Fig.  89  (2),  p.  145. 

These  strips  are  often  of  seasoned  and  varnished  maple;  but 
oak,  hornbeam,  and  ash  have  sometimes  been  used  instead.  The 
thickness  adopted  varies,  according  to  the  size  of  the  machine, 
between  the  limits  O'l  inch  and  0'2  inch. 

Binding  wires  are  usually  made  of  phosphor-bronze  or  steel. 
They  are  grouped  into  bands,  about  |  inch  wide.  Where  such 
bands  are  used  on  the  core,  a  channel  is  made  around  the  core  by 
inserting  a  sufficient  number  of  groups  of  core-discs  of  a  diameter 
slightly  smaller  than  that  of  the  armature.  The  depth  of  this 
channel  is  usually  •£$  inch  or  slightly  less.  Under  the  binding 
wires  is  laid  a  thin  ribbon  of  press-spahn  and  of  mica,  and  the 
individual  wires  are  at  intervals  soldered  together  and  clamped  by 
small  sheet  brass  or  copper  clips. 

The  size  of  binding  wire  can  be  calculated  from  the  strength  of 
the  wire,  and  the  centrifugal  force  to  be  provided  against.  The 


1  64     CONTINUOUS   CURRENT   MACHINE   DESIGN 


formula   is   directly   derived   from    the   ordinary   centrifugal   force 
expressions,  and  may  be  written  for  convenience  — 
Total  sectional  area  of  the")  _    /constant  X  total  weight  of  armature 
wires  in  all  the  bands    J  ""  \     coils  x  T)n2 

If  D  be  in  inches,  and  n  in  revolutions  per  second,  the  constant 
for  steel  or  phosphor-bronze  has  a  value  of  about  10~6,  which  allows 
a  stress  of  8000  Ibs.  per  sq.  inch  in  the  wire. 

Example.  —  A  ten-horsepower  motor  has  an  armature  11  inches 
diameter  which  runs  at  a  speed  of  750  r.p.m.  The  armature  is  wound 
with  369  turns  of  number  13  d.c.c.,  and  the  length  of  one  armature 
turn  is  35  inches.  Calculate  the  binding  wires. 

No.  13  d.c.c.  has  a  weight  of  about  80  Ibs.  per  1000  yds. 

369  x  35  x  80 

Hence  total  weight  of  armature  winding  =  —  ^  -  -mnn  —  =  29  Ibs. 

ob  X  1UUU 


Total  area  of  binding  wires  =  10'6  x  29  x  11  X  ~  X 

=  0*05  sq.  inch  . 

If  there  are  five  bands  of  twenty  turns  each,  the  area  of  one  wire 
is  0*0005  inch,  corresponding  to  No.  22  S.W.G.  approximately,  and 
the  width  of  each  band  will  be  |  inch  about. 

Commutator  Construction.  —  The  general  arrangement  and 
details  of  various  commutators  are  shown  in  Figs.  110,  111,  and  112. 


;*. 

FIG.  111.— HALF-SECTION  THROUGH  SMALL  COMMUTATOR  (THOMSON-HOUSTON  Co.) 

The  main  points  to  be  observed  are — 

(1)  That  the  commutator  can  be  removed  from  the  shaft  with- 
out disturbing  either  armature- winding  or  commutator-segments, 
except  in  so  far  as  the  connections  between  them  are  concerned. 


FIG.  110. — CYLINDER-WOUND  ARMATURE  WITH  COMMUTATOR 
(GENERAL  ELECTRIC  Co.). 


n 


B 


ISO  KW  GENERATOR  . 

EMM 


FIG.  112. — DETAILS  OF  A  COMMUTATOR  (CRAMP). 


[To  face  p.  164. 


GENERAL   MECHANICAL   CONSTRUCTION       165 


(2)  That  in  the  case  of  the  large  machine  the  commutator  is 
positively  driven  from  the  armature  hub. 

Details  of  construction,  showing  the  usual  angles  adopted,  to- 
gether with  the  method  of  fixing  the  risers  for  connection  to  the 
armature,  are  shown  in  Figs.  113  and  114.  These  risers  are  usually 
made  from  sheet  copper  (about  No.  20  gauge),  and  they  are  fixed  by 
rivets  and  solder  to  the  segments,  which  are  milled  away  to  receive 
them  as  shown  by  the  dotted  line 
in  Fig.  114,  the  armature  and  com- 
mutator when  fixed  appearing  as  in 
Fig.  110. 

A  marked  feature  of  modern 
commutators,  well  seen  in  the 
illustrations,  is  the  care  taken  to' 
ensure  as  much  ventilation  as 
possible.  The  passages  through 
the  commutator-bush  are  not  provided  solely  for  cooling  the  com- 
mutator, though  they  certainly  serve  this  purpose;  but  they  also 
admit  of  a  current  of  air  right  into  the  armature  itself.  The  air 
can  thus  be  drawn  in  at  both  ends  of  the  armature  and  expelled 


FIG.  113. — COMMUTATOR  SEGMENT. 


FIG.  114. — COMMUTATOR  SEGMENT  AND  RISERS. 

by  centrifugal  action  through  the  spaces  left  by  the  distance  pieces 
between  the  stampings.  The  connections  from  the  armature- winding 
to  the  risers  are  usually  well  soldered,  and  in  the  case  of  bar- wound 
armatures  they  are  also  riveted. 

Brush  Gear. — Brushes  are  either  fixed,  or  they  are  carried  by 
a  rocker  arranged  so  as  to  be  adjustable  about  the  commutator. 
The  former  plan  is  pursued  in  the  case  of  motors  which  must  be 
reversible,  like  those  for  tramcars  and  hoists ;  and  in  these  cases  the 
brushes  are  fixed  along  the  no-load  neutral  axis. 

Kockers  are  of  two  kinds :  those  which  are  carried  on  the  bearing- 
shell,  like  Figs.  115  and  116  ;  and  those  carried  by  the  field-frame, 
as  in  Figs.  117  and  118.  The  former  are  used  for  machines  up  tc 
about  50  K.W.,  and  the  latter  for  the  larger  sizes. 

The  turned  portion  of  the  bearing  upon  which  such  a  gear  as  that 


1 66     CONTINUOUS   CURRENT   MACHINE   DESIGN 

illustrated  iu  Figs.  115  and  116  would  fit  is  marked  with  the  letter 
A  in  Figs.  98  and  100.  Indeed,  Fig.  116  is  a  detail  of  the  actual  gear 
designed  for  the  machine  shown  in  Fig.  98.  The  adjustment  and 
fixing  of  the  gear  is  arranged  for  in  the  slot  B  in  Fig.  98,  through 
which  passes  a  set-screw  into  the  hole  B  of  Fig.  116.  The  gear  can 
thus  be  adjusted  and  locked  without  putting  a  spanner  inside  the 
case,  which  is  to  the  author  a  convenience  well  worth  attention. 
Fig.  118  is  a  scale  drawing  of  a  field  magnet  frame  and  brush-rocker 
of  the  type  illustrated  in  Fig.  117.  The  scale  of  the  drawing  can  be 
fixed  from  the  knowledge  that  the  armature  diameter  is  26  inches. 
The  machine  is  the  same  as  that  illustrated  in  Figs.  92  and  112. 

The  insulation  from  the   frame   of  the  brush-holders  and  their 
connections  has    already  been   referred   to  (p.  147).     It  is  usually 


FIG.  116.— DETAILS  OF  SMALL  BRUSH-ROCKER. 


carried  out  by  an  insulating  flanged  bush  which  separates  the 
spindles  carrying  the  brush-holders  from  "the  brush-rocker  itself, 
These  bushes,  as  seen  in  the  various  illustrations,  are  usually 
moulded  from  ambroin,  ebonite,  or  vulcanite;  sometimes  in  high- 
voltage  machines  they  are  made  up  from  micanite,  mica,  or  porcelain. 
A  dimensioned  detail  is  shown  in  Fig.  119. 

Brush-holders — The  only  brushes  now  used  upon  continuous- 
current  machines  are  made  of  some  form  of  carbon.  The  brush- 
holders  for  these  are  in  general  of  two  forms :  (a)  Box  type ; 
(b)  Lever  type.  It  is  quite  common  for  dynamo-makers  to  buy 
their  brush-holders  from  firms  that  have  specialized  in  this  line. 
This  Fig.  120  illustrates  the  brush-holders  of  Verity's,  Ltd.,  and 
Table  XVI.  gives  the  corresponding  standard  dimensions.  The 
three  upper  views  in  Fig.  120  show  the  construction  of  a  brush- 


FIG.  115. — BRUSH-GEAR  FOR  SMALL  MACHINE  (GENERAL  ELECTRIC  Co.). 


FIG.  1 17. —BRUSH-GEAR  FOR  LARGE  MACHINE  (GENERAL  ELECTRIC  Co.). 

[To  face  p.  166. 


GENERAL   MECHANICAL   CONSTRUCTION       167 

holder  for  very  small  machines.     In  such  cases  a  rocker  is  not  used, 
but  the  brushes  are  fixed  right  on  to  the  machine  end-plates.     In 


this  instance,  as  will  be  seen  from  the  illustration,  the  case  is 
moulded  from  an  insulating  material,  and  contains  a  rectangular 


i68     CONTINUOUS   CURRENT   MACHINE    DESIGN 


brass  tube  in  which  the  brush  slides.  The  spring  is  arranged  in  the 
space  above  the  tube,  and  is  of  the  spiral  type.  One  end  is  fixed 
inside  the  case,  and  the  other  is  connected  to  a  brass  rod  in  which 
the  carbon  brush  is  firmly  embedded.  A  flexible  lead  carries  the 
current  from  the  carbon  socket  to  the  brush  lead  terminal.  No 
current  passes  through  the  spring. 

The  desiderata  of  a  really  good  brush- 
holder  for  large  machines  are — 

(1)  The  moving  parts  should  be  light, 
so   that   the   brush  can   easily  follow  any 
small     irregularities     of    the     commutator 
surface. 

(2)  The  brush  should  be  automatically 
adjustable  for  wear,  and  should  feed  prac- 
tically radially. 

(3)  It  must  be  possible  easily  and  quickly 
to  adjust  the  brush  pressure. 

(4)  The   brush   should   possess   a   good 
FIG.  119.— DETAIL  OP       electrical  connection. 

BRUSH-ROCKER  INSULATION.  (5)  It  should  be  possible  to  change  the 

brush  quickly. 

These  points  are  most  easily  met,  so  the  author  thinks,  by  a 
brush-holder  of  the  box  type,  i.e.  of  a  holder  which  consists  of  a  box 
in  which  the  carbon  brush  slides  as  it  is  fed  forward  by  a  spring. 
Such  is  illustrated  in  the  middle  of  Fig.  120,  the  fourth  essential 
being  usually  provided  for  by  the  use  of  a  copper  "  pig-tail,"  or 
flexible  connection,  one  end  of  which  is  fixed  to  the  brush,  and  the 
other  end  to  the  holder.  Dimensions  of  this  type  of  holder  are  given  in 
Fig.  121  and  Table  XVI. 

Brush-holders  of  the  lever  pattern  to  fulfil  these  requirements 
are  somewhat  complicated,  and  must  be  made  in  thin  metal  or  in 
aluminium  for  condition  (1).  A  construction  is  clearly  indicated  in 
the  last  holder  shown  in  Figs.  120  and  121 ;  and  the  wavy  line  in 
Fig.  121  shows  the  copper  ribbon  used  to  unite  the  moving  and 
fixed  portions.  An  advantage  of  the  lever  type,  which  does  not 
apply  to  the  box  type,  is  in  the  firmness  with  which  the  brush  is 
held;  for  slight  movements  of  the  brush  which  tend  to  set  up 
sparking  and  rattling  are  frequently  met  with.  Swelling  of  the 
brush  with  heat,  and  consequent  binding  in  the  box,  is  a  trouble 
sometimes  met  with  in  brush-holders  of  the  box-type. 

Another  slight  advantage  of  the  lever  type  is  to  be  seqn  in 
Table  XVI.,  where  one  size  of  brush  only  is  used  for  all  machines, 
while  for  the  box-type,  the  Admiralty  have  no  less  than  five  standard 
sizes. 


FIG.  120. — STANDARD  BRUSH-HOLDERS  (VERITY'S,  LTD.). 

[To  face  p.  168. 


GENERAL   MECHANICAL   CONSTRUCTION        169 


FIG.  121. — DETAILS  OF  VERITY  BRUSH-HOLDERS. 

TABLE  XVI. 


Holder  Dimensions. 


uaroons. 

A. 

B. 

c. 

D. 

Box  Type. 

(Admiralty  sizes.) 

lV  X     f  X  IJ 

f/ 

ifV 

if 

Ii" 

5" 

i"  x  4"  x  i 

>r 

ii" 

if" 

4" 

V 
•fif 

l"x    l"xl{ 

i"  X  1"     X  IJ 

tt 
it 

ii" 
il'- 

I" 

1" 

" 
" 

r 

I- 

1"  x  IJ"  x  1} 

it 

i 

il" 

7" 

It" 

7" 

Lever  Type. 

-I"  x  f  x  1" 

3" 

If 

tt* 

7" 

8 

The  sketch  of  mechanical  details  here  given  is  necessarily  very 
incomplete.  More  may  be  seen  of  such  matters  by  a  few  days  in  a 
works  than  by  weeks  of  study  of  illustrations.  But  failing  the  former 
opportunity,  much  may  be  learnt  by  carefully  drawing  out  details 
from  actual  machines,  or  from  the  various  published  sheets  of 
drawings,  as  for  instance  those  by  T.  and  T.  G.  Jones.*  Several 
illustrations  in  the  present  chapter  have  been  taken  by  permission 
direct  from  the  last-named  authors,  as  it  is  hard  to  find  examples  more 
suitable  or  better  drawn. 

*  "  Machine  Drawing,"  Book  4,  Section  1.    T.  and  T.  G.  Jones.  .  London  and 
Manchester  :  John  Heywood. 


CHAPTER  XII 
COSTS 

IT  has  been  pointed  out,  and  there  is  much  truth  in  the  statement, 
that  estimating  the  cost  of  machines  has  been  too  much  divorced 
from  designing,  and  that  the  designer  has  not  sufficiently  considered 
the  cost  of  his  final  arrangement.  However  this  might  have  been 
in  the  past,  it  is  certain  that  present  competition  compels  the  strictest 
attention  to  the  cost  of  every  detail ;  and  each  designer  should  have 
some  ready  method  of  estimating  the  costs  of  his  designs  for  com- 
parative purposes,  so  that  he  may  only  put  forward  for  manufac- 
ture those  which  combine  economy  with  efficiency.  The  expression 
"  ready  method  "  is  used  advisedly,  for  no  designer  should  attempt 
to  displace  the  estimating  department :  on  the  contrary,  it  should 
be  the  duty  of  the  estimating  department  to  supply  the  designer 
with  such  figures  as  shall  enable  him  to  carry  out  his  relative 
costs  with  fair  accuracy. 

On  account  of  the  vast  differences  existing  between  works  in  size 
and  equipment,  it  is  hardly  possible  to  say  in  which  direction 
economy  must  always  lie ;  for  the  author  has  seen  processes  carried 
out  in  some  works,  which  in  others  would  be  entirely  inadmissible 
on  the  score  of  expense.  In  consequence,  the  most  that  can  be  done 
is  to  indicate  a  proceeding  which,  if  properly  carried  out  in  each 
individual  works,  will  lead  to  an  efficient  system  of  relative  costing 
for  different  designs. 

Whatever  system  of  time-sheets,  store-cards,  etc.,  may  be  adopted, 
the  costs  of  any  machine  are  finally  brought  together  on  to  a  sum- 
mary sheet  which  varies  but  little  in  even  very  different  works. 

Such  a  summary  sheet  is,  in  its  more  elaborate  form,  usually 
divided  into  three  main  portions,  viz.  Labour,  Material,  Miscellaneous. 
Each  of  these  is  again  subdivided. 

Under  Labour  is  found — 

1.  Machinemen. — To  the  cost  of  the  labour  under  this  head  is 
added  a  percentage  to  cover  supervision,  and  establishment  charges 
such  as  rent,  rates,  taxes,  lighting,  heating,  and  interest  and 


COSTS  171 

depreciation  on  the  cost  of  tools.  This  percentage  varies  from  40  to 
120  per  cent,  according  to  the  proportion  which  the  items  included 
bear  to  the  works  turnover.  It  can  only  be  determined  by  the 
auditors  at  the  annual  audit,  and  no  two  works  are  quite  alike. 

2.  Bench-hands,  such  as  joiners,  fitters,  pattern-makers,  smiths, 
hand-winders,  etc.  To  the  cost  of  labour  under  this  head  must  be 
added  a  percentage  similar  to  that  above,  but  smaller  in  value 
because  the  ratio  of  wages  per  hour  to  capital  costs  in  tools,  etc., 
involved,  is  much  greater.  Here  again  the  proper  proportion  to  be 
added  must  be  determined  by  the  auditors,  and  usually  ranges  from 
40  per  cent,  to  70  per  cent. 

Under  Material  is  found — 

Castings,  rough  material  from  stores,  finished  material  from 
stores  (bolts,  screws,  wire,  insulating  tubes,  etc.),  timber,  etc.  To 
all  material  bought  in  this  way  is  added  a  small  percentage  to  cover 
the  cost  of  handling,  usually  about  5  per  cent.  Some  firms  add  7J 
per  cent. 

Under  Miscellaneous  is  found  testing,  special  fittings,  and 
special  expenses  not  included  under  labour  or  material. 

To  the  cost  of  the  article  as  determined  by  the  sum  of  the  above 
items  (called  the  total  works-cost)  two  more  percentages  must  be 
added  before  the  selling  price  is  arrived  at.  One  of  these,  which 
varies  enormously  in  different  cases,  is  intended  to  cover  selling 
expenses,  such  as  advertisement,  agents,  commissions,  branch-office 
costs,  etc.,  and  the  other  is  profit. 

Calculation  of  Total  Works-Cost. — From  summary  sheets 
drawn  up  on  the  above  lines  it  is  possible  to  deduce  a  further 
summary,  in  which,  for  each  special  article,  the  relationship  of 
labour  and  material  to  material  can  be  ascertained.  This  gives 
the  total  works-cost  of  the  article  when  once  the  material  involved 
is  known.  Now,  the  latter  bears  a  fairly  constant  ratio  to  the 
cost  of  "  effective  material " ;  i.e.  to  the  total  cost  of  all  the  iron 
and  copper  involved  in  the  magnetic  and  electric  circuits  of  the 
machine.  Thus,  if  these  be  calculated,  the  total  works-cost  can  also 
be  estimated.  It  is  seen  that  all  that  is  required  to  enable  the 
designer  to  compare  costs  of  different  designs  is  the  ability  to  cal- 
culate the  effective  material  and  its  cost,  and  a  knowledge  of  the 
connection  between  this  material  and  the  labour  expended  upon  it 
as  given  by  the  summary  sheets  above  referred  to. 

Some  estimators  use  a  much  more  simple  method  for  deter- 
mining the  selling  price.  Thus  they  may  add  all  the  labour-costs 
plus  a  percentage,  and  all  the  material- costs  plus  5  per  cent.,  and 
to  the  sum  of  these  add  a  percentage,  say  10  per  cent.,  for  profit. 
In  this  case  the  establishment  and  selling  charges  all  appear  in 
the  one  percentage  on  labour,  which  then  mounts  up  to  sometimes 


172     CONTINUOUS   CURRENT   MACHINE  DESIGN 

200  per  cent.,  on  to  which  is  added  the  cost  of  material  +  5  per 
cent.,  and  to  the  total  the  percentage  for  profit. 

The  percentages  above  mentioned,  whilst  they  no  doubt  bear 
excellent  testimony  to  the  reduction  of  labour- costs  under  modern 
competitive  industrial  conditions,  yet  testify  also  to  the  extra- 
ordinary cost  of  persuading  a  customer  to  take  the  article  when  once 
it  has  been  manufactured.  Thus  keen  competition,  whilst  tending 
towards  efficient  production,  leads  also  to  extravagant  methods  of 
distribution  and  exchange ;  from  which  it  would  seem  that  a  reason- 
able reduction  in  competition  might,  if  properly  controlled,  admit 
either  of  an  increase  in  labour-payments  on  the  one  hand,  or  of  a 
substantial  advantage  to  the  consumer  on  the  other. 

Examples  of  Costing. — To  illustrate  the  methods  of  costing 
above  set  forth  consider  the  following  case : — 

The  cost-cards  for  the  armature  and  shaft  of  a  250  K.W.  500-volt 
moderate-speed  generator  yield  the  following  summary  : — 

Labour. 

£      s.     d.       £      s.     d.        £       s.     d. 

Machinemen      .         .         .         600 
100  per  cent.     .         .        .         600 

12     0     0 


Bench  hands      .         .         .         300 
Winders  13     0     0 


16     0     0 
50  per  cent.        .         .         .         800 

24     0     0 


Total  labour       .  .                                   .         .  36     0     0 

Material. 

Steel  shaft          .         .  900 

Laminations       .         .  40     0     0 

Copper      .         .         .  .       20     0     0 

Insulating  material    .  .         700 

Spider        .         .         .  .         400 

Nuts,  bolts,  binding-wire,)  ^     ^     Q 

i  " 


and  miscellaneous 


90     0     0 

5  per  cent.          .         .         .         4  10     0 
Total  material  costs    ......  94  10     0 

Total  works  cost  of  armature      .        «,         .         .         130  10     0 


COSTS  173 

In  like  manner,  from  similar  summaries  of  the  other  parts  of  the 
same  machine  the  following  figures  are  obtained : — 

Total  works  cost  of  magnets,  yoke,  bearings  and         £       s.   d. 

field  coils         .     -....'• 250     0     0 

Total  works  cost  of  commutator  and  brush  gear  .         160     0     0 

Total  works  cost  of  whole  machine       .         .         .         540  10     0 

Now  suppose  that  the  designers  in  the  works  where  the  above 
machine  is  made  are  asked  to  get  out  designs  for  500-volt  machines 
of  other  sizes.  Suppose,  also,  that  they  have  access  to  the  summary 
sheets  mentioned  above.  Then  from  these  they  take  first  the  cost 
of  the  effective  material  as  follows  : — 

Iron — 


Yoke    . 

£ 
30 

s. 

0 

d. 
0 

£ 

s.      d. 

Poles  and  shoes 

. 

. 

24 

0 

0 

Armature  core 

ter  — 

• 

• 

40 

0 

0 

94 

0     0 

Armature 

. 

. 

20 

0 

0 

Shunt-field   . 

. 

. 

50 

0 

0 

Compounding 
Commutator 

Total  cost  of  effective 

material 

8 
45 

0 
0 

0 

0 

123 

0     0 

217 

0     0 

TCfltin 

total 

works  cost 

540 

2-46 

cost 

of  effective  material 

217 

If  other  sizes  of  machines  can  be  similarly  analyzed,  a  rough  curve 
can  be  plotted  between  the  above  ratio  and  the  kilowatts  output  per 
revolution  per  minute,  from  which  approximate  values  for  the  ratio 
in  the  case  of  the  machines  to  be  designed  can  be  obtained.  If 
great  care  is  taken  in  reducing  the  machining  as  well  as  the  effective 
material,  a  change  in  the  ratio  may  be  found  when  the  first  machine 
goes  through  the  shops,  and  this  change  may  be  allowed  for  in  sub- 
sequent designs,  so  that  a  better  approximation  is  obtained  at  each 
stage,  new  curves  being  finally  constructed.  In  any  case,  so  long  as 
even  approximate  values  for  the  above  ratio  are  known,  the  designer 
can  compare  his  preliminary  trial  designs  with  the  selling  prices  of 
similar  machines  by  other  makers,  until  he  arrive  at  a  machine 
which,  for  the  same  price,  has  some  advantages  over  that  of  his 
competitors. 

Values  of  Cost- Ratios.— Where  no  such  ratio  can  be  obtained, 


174     CONTINUOUS   CURRENT   MACHINE   DESIGN 

the  following,  taken  from  the  practice  of  a  certain  works,  may  be 
used  as  a  rough  guide  or  check : — 

TABLE  XVII. 


K.W.  output. 

E.P.M. 

total  works  cost 

cost  of  effective  materal' 

500 

250 

2 

300 

300 

2-35 

200 

400 

2-5 

100 

450 

2-8 

80 

500 

3 

60 

600 

3-2 

40 

700 

) 

20 

800 

3-4* 

10 

800 

) 

The  following,  for   another   works,  give   values   for   short-rated 
totally  enclosed  series  crane  motors : — 

TABLE  XVIII. 


B.H.P. 
per  rev.  per  min. 

R    .            total  works  cost 

cost  of  effective  material* 

o-oi 

3 

0'02 

2-8 

0-04 

2-4 

0-06 

2 

0-08 

1-9 

012 

1-8 

016 

1-6 

Costs  of  Effective  Material. — In  calculating  the  cost  of  the 
effective  material,  the  parts  considered  are  those  given  in  the  example 
on  p.  173.  The  weights  of  these  parts  are  easily  deduced  from  the 
design,  and  at  the  present  time  the  following  prices  are  representative 
in  England : — 

*  These  values  vary  enormously,  according  to  the  number  of  machines  of  one 
size  put  through  at  one  time. 


COSTS  175 

Iron  and  steel — 

Armature  stampings          .         .         .  4d.  to  5d.  per  Ib. 

Pole-face  stampings           .         .         .  2^d.  „ 

Iron  castings \<L,  „  \\d.  „ 

Steel  castings  .         .         .         .         .  23.     „  %\d.  „ 

Mild-steel  and  wrought-iron  bar,  etc.  l^d.  „  l\d.  „ 

Copper — 

Wire  for  magnets  and  small  armatures      9d  ,,  I/-  „ 

Strap  for  armatures  and  series-windings   $d.  „  Wd.  „ 

Commutator-sections        .         .         .       lid.  „  I/-  „ 

Naturally  all  these  prices  will  vary  with  the  market  for  the 
material ;  the  small  variations  shown  are  due  in  the  case  of  castings 
to  the  cost  of  moulding,  or  to  the  difficulty  of  the  pattern ;  and  in 
the  case  of  wire  to  the  size  of  the  wire,  i.e.  to  the  labour  entailed  in 
drawing.  In  the  case  of  stampings,  the  cost  of  the  tools  and  the  waste 
material  have  to  be  considered.  Armature  stampings  are  usually 
No.  26  gauge,  and  pole-face  stampings  No.  20  or  21.  Examples  of 
the  cost  of  effective  material  are  given  on  pp.  188,  196,  and  210. 

Other  Methods  of  Costing. — Although  the  foregoing  may  seem 
only  a  rough  and  ready  method,  yet  still  simpler  plans  have  been 
proposed  and  used.  Thus  Hobart  suggests  two  formulae  with  con- 
stants which  are  exceedingly  simple.  In  the  first,  he  adds  to  the 
cost  of  the  effective  material  a  sum  which  he  calls  the  non-effective 
cost,  and  which  may  be  expressed  in  the  form — 

(constant)D!2  -f  (constant^!, 

where  D!  is  the  diameter  outside  the  yoke.  DI  and  L  are  in  centi- 
metres. These  constants,  of  course,  must  be  derived  for  each  works, 
but  in  one  instance  they  are  quoted  as  0*1  and  0*14  respectively.* 

His  second  method  is  still  more  brief,  for  he  writes  it :  (constant) 
X  DLb  where  LI  is  the  length  of  the  armature  over  the  end  connec- 
tions, and  consequently  may  be  written  roughly  as  * — 

I,-    *»    +  L 

4  poles 

Such  methods  can  only  be  relied  upon  when  a  large  number  of 
machines  enable  the  constants  to  be  very  closely  determined.  Other 
methods  have  been  suggested  by  E.  K.  Scott,  Mavor,  Wilson,  and 
others.t 

Cost  of  Component  Parts. — It  is  generally  impossible  to  form 
an  estimate  of  the  cost  of  the  field-magnet  or  armature  until  the 
preliminary  design  is  fairly  complete.  With  the  commutator, 

*  H.  M.  Hobart,  Electrician,  vol.  51,  p.  850. 

t  See  Jour.  Inst.  E.E.,  p.  400,  1893  ;  and  p.  160,  1897. 


176     CONTINUOUS   CURRENT   MACHINE   DESIGN 

however,  this  is  not  the  case,  as  its  cost  depends  chiefly  upon  the 
current  to  be  collected. 

Cost  of  Commutators. — It  has  been  already  pointed  out  that  the 
radial  depth  of  commutator  copper  varies  but  little,  even  over  a  wide 
range  of  sizes.  Perhaps  it  may  most  conveniently  for  present  pur- 
poses be  taken  at  2".  It  is  then  clear  that  the  cost  of  the  commu- 
tator is  almost  independent  of  any  factors  other  than  current  to  be 
collected  and  peripheral  speed.  Thus,  if  we  assume  an  average  value 
of  30  amps,  per  square  inch  for  the  current-density  under  the  brush, 
the  total  commutator  losses  may  be  put  into  terms  of  the  current  to 
be  collected  and  the  peripheral  speed  (Vc).  From  p.  133  we  ob tain- 
Electrical  losses  +  friction  losses  =  total  current  (1'8  +  0'000678YC) 
Area  of  necessary  cylindrical  J 

radiating  surface  (from  p.  86)     =  total  current  (045  +  0'00017VC) 

allowing  4  watts  per  sq.  inch  j 

This  radiating  surface  multiplied  by  the  average  depth  of  say  2" 
gives  a  first  approximation  to  the  volume  of  active  copper  in  the 
commutator,  so  that  the  cost  at  I/-  per  Ib.  will  be — 

Total  current  (0-27  +  0'0001VC)  shillings 

which  corresponds  to  about  1*8^.  for  each  watt  dissipated.  This 
value  usually  lies  between  l'2d.  and  2^d.  according  to  the  depth  of 
segment  and  the  watts  per  square  inch  allowed.  The  cost  of  the 
commutator  increasing,  as  shown,  with  increase  of  current,  tends  to 
make  low- voltage  machines  cost  more  than  high- voltage  machines  of 
similar  output.  This,  however,  is  often  offset  by  decreased  insulation 
and  winding  costs,  so  that  as  a  general  rule  there  is  little  difference 
in  cost  between  200-  and  500-volt  machines.  Outside  these  limits 
the  relative  cost  depends  upon  the  size  of  the  machine  ;  for  in  small 
machines  the  number  of  commutator  sizes  stocked,  the  available  length 
of  frame,  etc.,  will  obviously  affect  the  range  of  voltages  over  which 
the  design  can  be  used  with  economy.  Larger  machines,  on  the  other 
hand,  can  be  considerably  altered  in  detail  to  suit  special  outputs 
without  greatly  increasing  the  cost  of  manufacture,  because,  as  has 
been  seen,  the  ratio  of  total  works-cost  to  cost  of  material  is  so 
much  smaller. 

General  Effects  of  Design  Ratios  upon  Cost. — One  of  the 
best  indications  of  excellence  of  design  as  regards  cost  is  the  ratio 
amporo  turna  per  pole  x  number  of  poles  divided  by  total  armature 
ampere-conductors.  The  values  of  this  ratio,  which  correspond  to 
minimum  cost,  have  already  been  referred  to  on  p.  62,  but  the  figures 
there  given  depend  very  much  upon  the  type  of  machine,  and  can  rarely 
be  approached  except  when  interpoles  are  employed.  For  traction 
generators  without  interpoles  the  ratio  will  often  lie  between  600 
and  800,  because  of  the  large  number  of  commutator  sections 


COSTS 


177 


necessitated  by  a  lower  value  of  the  commutation  constants.  In  the 
comparative  calculation  carried  out  on  pp.  189,  196,  the  effect  of 
commutation  constants  upon  the  ratio  is  clearly  seen,  and,  generally 
speaking,  so  much  depends  on  the  purpose  for  which  the  machine  is 
intended,  on  its  voltage,  speed,  and  rating,  that  it  is  impossible  to 
lay  down  hard-and-fast  lines  without  a  very  definite  specification 
to  work  to.  One  may  say,  however,  with  comparative  certainty, 
that  the  interpole  machine  with  lowest  total  works-cost  does  lie 
somewhere  within  the  limits  named  on  p.  62  ;  and  for  machines 
without  interpoles  the  following  table  is  typical  of  good  modern 
practice : — 

TABLE  XIX. 

NON-lNTERPOLE   MACHINES. 


Y 

Value  of  ratio  -=.. 

K.W.  output. 

X 

Low  speed. 

High  speech 

10 

550 

650 

50 

500 

750 

100 

500 

850 

250 

600 

950 

500 

800 

1100 

1000 

850 

1200 

1500 

900 

1200 

In  considering  this  ratio  it  must  always  be  remembered  that  few 
designers  are  called  upon  to  consider  a  frame  for  one  single  out- 
put unless  it  be  for  a  large  and  special  machine.  A  machine  of 
given  core-length  for  a  certain  speed  will  have  that  core-length 
increased  in  almost  inverse  proportion  for  lower  and  higher  speeds,  so 
that  the  above  factor  will  be  changed  according  to  that  speed,  and  it 
is  from  this  point  of  view  that  designing  from  such  a  ratio  is  most 
unsatisfactory,  and  would  be  entirely  out  of  the  question  were  it  not 
for  the  comparatively  small  variation  between  small  and  large 
machines.  It  must  not  be  supposed  that  the  limits  above  given 
by  any  means  represent  universal  practice ;  indeed,  the  author  could 
quote  cases  in  which  for  150  K.W.  machines  the  ratio  was  as  high 
as  1200,  but  he  does  not  consider  that  such  designs  could  be  very 
economical. 

Generally  speaking,  it  may  be  said  that  increasing  the  flux  per 
pole  increases  the  constant  losses,  and,  up  to  a  certain  limit,  also  the 

N 


178     CONTINUOUS   CURRENT   MACHINE   DESIGN 

costs.  It  has  the  effect,  too,  of  lowering  the  efficiency  at  low  ratings, 
and  so  unfits  the  machine  for  work  when  totally  enclosed.  It  is 
true  that  it  tends  to  raise  the  efficiency  somewhat  at  high  ratings, 
but  the  gain  in  this  respect  does  not  counterbalance  the  disadvantages 
mentioned. 

A  small  flux  per  pole  is  therefore  desirable  for  most  purposes, 
and  especially  so  where  the  machine  must  be  sometimes  totally 
enclosed.  The  comparative  value  of  the  flux  is  obviously  measured 
by  the  ratio  dealt  with  above,  and  the  possibility  of  decreasing  it 
is  checked  in  non-interpole  machines  by  the  great  increase  in  the 
armature  diameter,  and  in  interpole  machines  by  the  gradually 
increasing  cost  of  the  interpoles. 

Other  points  which  influence  the  cost  are :  (1)  the  rating  of  the 
machine,  and  the  amount  of  ventilation;  (2)  the  voltage  of  the 
machine,  and  consequent  possible  space  factor ;  (3)  the  speed  of 
the  machine. 

The  first  of  these  has  been  dealt  with  under  Temperature  Eise 
(Chaps.  VI.  and  VII.)  and  under  Division  of  Losses  (Chap.  III.). 
We  may  here  add  that  when  the  machine  is  totally  enclosed  and 
short-rated,  the  mass  of  the  frame  often  has  more  to  do  with  the 
temperature  rise  than  has  the  radiating  surface.  It  is  impossible  to 
properly  design  short-rated  motors  until  some  agreement  is  reached 
as  to  the  tests  which  they  should  be  called  upon  to  fulfil ;  an 
example  dealing  with  such  a  machine  is  given  on  p.  213.* 

Often  a  designer  will  find  himself  confronted  with  the  relative 
effect  upon  the  cost  of  two  dependent  variables ;  thus  reducing  the 
section  of  a  yoke  will  increase  the  amount  of  field  copper,  but 
decrease  the  weight  of  steel  or  iron  required,  and  the  question  is, 
What  section  of  yoke  should  be  adopted  ?  The  point  can  often  be 
decided  algebraically  by  obtaining  an  equation  connecting  the  two 
quantities,  and  finding  the  minimum  of  the  sum  of  the  two. 
More  often  the  expression  is  too  complicated  to  be  of  any  use,  and 
then  a  graph  of  the  two  quantities  plotted  upon  the  same  sheet 
may  be  used  for  determining  the  sum  of  the  two.  Thus  Fig.  122 
gives  the  cost  of  steel  and  copper  respectively,  plotted  against  the 
density  in  the  yoke  in  lines  per  square  inch  for  a  60  K.W.  machine 
at  460  E.P.M.  The  economical  density  in  this  case  is  about  87,000 
lines  per  square  inch,  and  as  this  is  below  saturation  it  is  a  possible 
density.  By  such  means  the  cost  of  existing  machines  may  frequently 
be  considerably  reduced. 

We  may  conclude  by  collecting  a  few  of  the  more  important 
considerations  affecting  cost,  and,  as  usual,  these  will  be  put  under 
the  headings  of  Small  Machines  and  of  Large  Machines. 

*  See  a  recent  paper  by  Dr.  Pohl,  Electrician,  March  25,  1910. 


COSTS 


179 


(a)  Small  Machines. — For  each  part  the  very  best  material  of  its 
kind  should  be  specified,  and  the  amount  of  machining  should  be 
reduced  to  a  minimum,  except  in  those  cases  where  absence  of 
machining  would  entail  extra  hand  labour ;  as,  for  instance,  in  the 
case  of  a  shaft,  which  it  is  often  more  economical  to  turn  out  of  a 
large  bar,  leaving  the  necessary  collars,  than  to  make  approximately 
to  shape  as  a  forging  to  be  afterwards  turned. 

Eemember  the  necessity  of  flexibility  of  design,  especially  as 
regards  the  length  of  armature  and  commutator  for  high  and  low 
voltages  (p.  33).  Kemember,  also,  that  variations  in  speed  can  be 
largely  allowed  for  by  the  method  of  lengthening  and  shortening  the 
armature,  and  in  the  case  of  very  high  speeds,  by  the  addition  of 
interpoles. 

Very  small  machines  in  which  it  does  not  pay  to  vary  armature 


78 


84 


90  Density 

Lines  per  sq.  in.  -f- 103. 
Fig.  122. — METHOD  OF  DECIDING  BEST  YOKE-SECTION. 

and  commutator  lengths  most  usually  have  their  output  reduced 
as  the  voltage  is  raised,  and  slight  advantages  may  sometimes  be 
gained  by  changes  in  the  ampere- turns  per  pole  and  in  the  efficiency. 
Naturally  also  in  these  cases  the  output  will  change  with  the 
speed.* 

For  appearance'  sake  some  makers  will  put  the  pole  nearer  to 
one  end  of  the  yoke,  as  this  has  the  effect  of  causing  the  commutator 
to  stand  out  less ;  such  an  arrangement,  however,  renders  the  machine 
impossible  as  a  rotary  converter  or  double-commutator  machine 
without  a  fresh  pattern  for  the  end-plate. 

(&)  Large  Machines,  being  much  less  dependent  upon  labour  cost, 
can  be  varied  within  wider  limits.  Thus  the  number  of  poles  may 

*  For  a  full  discussion  of  these  points,  see  Ekctrial  Engineering,  vol.  i.  p.  52, 
January  10,  1907. 


i8o     CONTINUOUS    CURRENT   MACHINE   DESIGN 


be  increased  as  the  current  increases,  but  otherwise  the  advantages 
obtained  by  altering  the  armature  and  commutator  lengths  are 
similar  to  those  mentioned  under  (a).  Flexibility  is,  however,  less 
important,  and  distribution  of  material  more  important.  Consequently 
it  is  necessary,  after  working  out  a  preliminary  design  with  satis- 
factory proportions,  to  vary  these  by  many  subsequent  trial  designs, 
until  the  minimum  cost  that  is  consistent  with  good  performance  is 
obtained. 

Tendency  of  Modern  Manufacture. — The  necessity  for  sparing 
no  effort  to  arrive  at  the  very  best  possible  compromise  between  per- 
formance and  cost  has  been  frequently  emphasized  in  the  preceding 
pages.  No  text-book,  however  complete  and  however  well  conned,  can 
possibly  enable  a  designer  to  dispense  altogether  with  the  experience 
necessary  for  successful  competition,  chiefly  because  of  the  different 
conditions  existing  in  different  works.  But  should  the  truth  of  this 
statement  be  yet  held  in  doubt,  eloquent  testimony  is  to  be  found  in 
a  bald  comparison  of  the  conditions  existing  only  a  few  years  back 
with  those  which  obtain  to-day  (1910).  Thus  the  following  table, 
though  it  refers  to  one  size  only,  is  typical  of  what  has  taken  place 
throughout  the  whole  of  the  industry  : — 

TABLE  XX. 

COMPARISON   OF   COSTS    AND   PRICES  FOR  A   SEMI-ENCLOSED   CON- 
TINUOUS-CURRENT MOTOR  OF  7  B.H.P.  AT  750  REVS.  PER  MIN. 

SUITABLE   FOR  460   VOLTS. 


Year. 

Cost  of 
Material,  etc. 

Cost  of 
Labour,  etc. 

Total  Works- 
cost. 

Selling 
Price. 

Profit  per  cent, 
of  Works-cost. 

1902 

£ 

22 

£ 
22 

£ 

44 

£ 
56 

Per  cent. 

27 

1910 

15 

10 

25 

30 

20 

Thus  in  eight  years  (for  this  size)  has  the  material  been  reduced 
by  nearly  32  per  cent.,  the  labour  charges  by  55  per  cent.,  the  total 
works-cost  by  43  per  cent.,  and  the  profit  by  58  per  cent.  And  yet 
the  efficiency  is  at  least  as  high  as  before,  and  wages  have  risen 
rather  than  decreased.  The  tendency  thus  manifest  is  still  to  be 
traced  in  catalogues,  tenders,  and  balance-sheets. 


EXAMPLES  OF  PEOCEDUEE  IN  DESIGN 


THE  object  of  the  examples  which  follow  is  to  illustrate  the  bearing  of 
the  many  considerations  discussed  in  the  preceding  chapters.  It  should 
be  very  apparent  that  the  design  for  a  dynamo  or  motor  can  at  best 
only  be  a  good  compromise;  and  that  the  very  data  available  are, 
even  for  machines  of  the  same  output,  dependent  upon  factors  of  a  very 
indeterminate  nature,  such  as  position  of  works,  price  of  raw  material, 
size  of  works,  number  of  machines  of  one  output  required,  and  many  other 
questions.  For  these  reasons  it  is  desirable  that,  having  paid  attention 
to  the  many  conflicting  conditions  mentioned,  each  designer  should  formu- 
late for  himself  a  method  of  attacking  the  problems  he  is  called  upon  to 
solve.  Reliance  upon  a  definite  set  of  formulae  is  apt  to  lead  to  neglect  of 
the  conditions  upon  which  such  expressions  are  based,  so  that  on  a  return 
to  root  principles  it  may  be  found  that  some  important  ratio  involved 
in  the  algebra  has  been  lost  sight  of.  In  the  author's  opinion,  sets  of 
equations  are  generally  only  of  value  to  the  man  who  put  them  together 
for  his  own  use. 

The  illustrations  given,  therefore,  will  be  such  as  to  indicate  (i.)  methods 
of  arriving  quickly  at  the  outline  of  a  satisfactory  design  •  and  (ii.)  the 
directions  in  which  the  work  on  this  first  outline  should  proceed  in  order 
to  arrive  at  a  final  form. 

It  is  possible  broadly  to  discriminate  between  two  classes  of  machine, 

vlZ» 

1.  Small  machines. 

2.  Large  machines. 

By  small  machines  we  mean  such  sizes  (usually  less  than  30  K.W.)  as 
are  never  manufactured  one  at  a  time.  These  must  be  considered,  there- 
fore, from  various  standpoints,  as,  for  instance,  adaptability  to  various 
voltages  and  speeds,  possibility  of  enclosing,  and  output  when  enclosed. 

By  large  machines  we  mean  those  which  may  fairly  be  considered  as 
individual  designs. 

In  regard  to  the  first  class,  it  has  already  been  pointed  out  that  great 
divergence  of  opinion  exists  as  to  the  proportions  and  densities  to  be 
employed,  so  that  in  order  to  commence  a  design  it  is  often  necessary  first 
to  find  out  in  which  direction  modern  machines  are  tending ;  next,  to  rough 
out  a  trial  design ;  and,  finally,  to  correct  this  for  flexibility  of  output  and 
cost  of  production. 

In  both  classes  we  can  discriminate  between  machines  intended  for 


1 82     CONTINUOUS   CURRENT   MACHINE   DESIGN 


constant  pressure  (i.e.  shunt  and  compound  dynamos  and  motors)  and 
those  intended  for  varying  pressures — usually  series  wound.  The  latter 
are  generally  ruled  by  considerations  which  do  not  occur  with  the  former, 
and  consequently  they  will  be  treated  separately. 

Constant  Pressure  Machines.  Problem  i. — Let  it  be  sup- 
posed that  a  line  of  small  motors  is  required  ranging  from  5  to  15  H.R, 
and  that  it  is  proposed  first  to  consider  a  machine  of  about  12  H.P., 
running  at  900  r.p.m.  (  =  15  r.p.s.) 

We  may  first  analyze  a  few  designs  of  such  machines  by  competing 
makers,  such  as  the  three  given  below — 

TABLE    XXI. 


Details. 

A. 

B. 

C. 

H.R 

5 

10 

5 

R.p.m. 

600 

950 

700 

Voltage    . 

220 

500 

110 

Type 

Semi-enclosed 

Semi-enclosed 

Totally  enclosed 

Material  of  yoke 

0.1. 

C.S. 

C.S. 

Field-poles 

c.s. 

C.S. 

C.S. 

Armature  winding   . 

2-circuit 

2-circuit 

2-circuit 

Armature  diameter  . 

9" 

9f 

10" 

No.  of  poles 

4 

4 

4 

Gross  length  of  core 

4f" 

6|" 

6" 

One  space  y\ 

Ventilation 

None 

wide      right! 
through  thej 

One  space 
f  "  wide 

armature      j 

Slot  depth 

1" 

0-8" 

0-625" 

No.  of  slots 

31. 

47 

64 

Pole-arc  length 

51" 

5f 

5" 

Length  of  air-gap 

0-15" 

0-125" 

0-15" 

From  such  data  some  general  probabilities  may  be  gleaned  which  will 
afterwards  be  of  use.  For  instance,  in  this  case  the  number  of  poles  to 
try  is  evidently  4,  and  the  armature-winding  will  be  best  as  two-circuit. 

The  next  step  may  be  to  decide  a  few  general  points  from  which  a 
number  of  designs  may  be  quickly  outlined.  We  may  take — 

Yoke  .         .     Cast  iron,  with  a  density  of  about  35,000  lines  per  sq.  in. 
Pole    .         .     Caststeel,      „  „    '  „    100,000 

Pole-face     .     Laminated     ,,    a  face  density  of      45,000         ,,  „ 

Tooth-roots      Laminated,  uncorrected  density  of  150,000         „  „ 

Armature  below  teeth,  with  a  density  of    .         .     85,000         „  „ 

X  assumed  1  '25. 


EXAMPLES   OF   PROCEDURE   IN   DESIGN         183 

Space  factor  for  440  volts,  0-24  (cf.  p.  147) 
200     „      0-28  (cf.  p.  147) 
Vr,  with  hard  brush  2 

pole  arc 

Section  of   pole,  circular.     Ratio  -*5  -  r—  r  =  0'7 

pole-pitch 

Efficiency  at  full  load,  86  per  cent.  (cf.  p.  27) 
Temperature  rise,  40°  C.    p  =  78  x  10  ~8 

We  assume  the  most  important  relationships  in  the  design  to  be  — 

Y 

The  ratio  ^  . 

The  value  D2L. 
The  value  Vr. 
Temperature  rise. 
Division  of  losses. 

General  Relationship  in  Terms  of  d.  —  Given  the  equation  on 
p.  128,  any  one  of  the  above  relationships  can  be  put  in  terms  of  the  pole- 
diameter,  or  the  armature  diameter.  This  the  reader  can  carry  out  for 
himself,  if  he  wishes  to  ;  we  have  already  given  reasons  for  not  doing  it. 
He  might  find,  however,  values  somewhat  as  follows  :  — 

14  t.p.s.  watts 

Y  =  Trd2  x  108  yr  = 


D2L  =  6'45d:{      Copper  loss  in  armature  =  -  -  ^  — 

•pip      nr\ 

Iron  losses  =  3  -Id3  X  =  -  ^  — 

Trd* 

and  so  on.     The  value  of  these  is  in  some  cases  considerable.     Thus,  see 

Y 
how  quickly  the  ratio  ^=  will  change  as  regards  the  pole  diameter. 

.A. 

Division  of  Voltage  and  Current.  —  As  suggested  on  p.  33,  we 
may,  if  necessary,  adjust  the  length  of  armature-core  and  commutator  to 
suit  the  voltage  and  current.  We  will  therefore  commence  the  design  for 
a  medium  voltage,  such  as  200  to  250. 

The  output  then  is  about  8950  watts  ;  input  =  10,400  watts. 

Total  cur  rent  =  say  41*6  amps.  @  250  volts. 

The  flux  per  pole  x  number  of  poles  is  evidently  Trd2  x  103,  where  d  is 
the  pole  diameter. 

The  active  wires  (w)  on  the  armature  for  a  two-circuit  winding  will 
be,  from  the  E.M.F.  formula  — 

108.60.E.4 

w  = 


2  .  900  .  Trd2 .  105 


0 
The  current  per  wire  is  x- 


1 84    CONTINUOUS   CURRENT   MACHINE   DESIGN 

Thus— 

Cw  __  x  _  EC   400 

Y      e^4 . 10s 


and  X~    400EC 

which,  as  being  independent  of  current  and  voltage,  is  a  very  useful 

expression. 

In  the  present  instance  EC  is  the  armature  output,  which  will  be  the 
total  input  minus  the  copper  loss  and  the  field  loss.  The  latter  we  do  not 
know,  but  we  may  for  present  purposes  take  a  value  from  Fig.  20,  say 
about  3  per  cent,  or  300  watts.  Afterwards  this  may  be  modified. 

Again,  from  the  curve  Fig.  21  we  see  that  the  armature  copper  loss 

3  *5 
will  be  about  3£  per  cent.,  so  that  the  corresponding  voltage  drop  is  -=^- 

X  250  =  8-8  volts;  and  the  voltage  drop  at  the  brushes  (Fig.  80)  =  2-4 
volts  total.  Therefore  the  E.M.F.  to  be  generated  by  the  armature  at  full 
load  =  250  -  (8-8  -f  2 -4)  =  say  238  volts,  and  EC  =  about  9700  watts. 

Now,  from  Table  XIX.  we  select  a  trial  value  for  ^ . 

We  know  that  the  value  should  be  as  low  as  is  possible,  and  we  there- 
fore decide  first  to  try  550. 

Thus  inserting  in  the  formula — 

Y 


_ 
X~  400EC 

Y 

the  values  for  ^  and  EC,  we  get  d  =  4-4",  or  say  : — 

(1)  d  =  ty 

(2)  Area  of  pole  core  section  =  16  sq.  ins. 

(3)  Flux  per  pole  =  16  X  105 

(4)  Flux  issuing  from  shoe  =  12-8  x  106  lines 

12*8  x  105 

(5)  Area  of  shoe  face  =     45  QQQ"  =  28'5  scl- ins- 

(6)  Axial  length  of  shoe  =  L  =  4J"  say  (cf.  p.  20) 

(7)  Pole-arc  =  6-3" 

4x6-3      ,-,,. 

(8)  Armature  diameter  =     Q.^    =11$' 

(9)  Ratio  ?jp  =  1-56  (cf.  p.  20) 

(10)  Total  armature  conductors  (2-circuit)  =  620 

(11)  Amp.  wires  per  inch  periphery  =  355 

(12)  D2L 

In  the  formula  on  p.  15,  adopting  m^  =  1*1,  m^  =  1,  then — 

K  =  0-34 

(13)  Depth  of  slot  =  -08D  =  0'92"  * 

*  Note  that  this  may  sometimes  be  increased  by  3y,  as  on  p.  191. 


EXAMPLES   OF   PROCEDURE   IN   DESIGN        185 

Aggregate  area  of  all  the  slots  =  J  armature  circumference  x  0'92 

=  16*6  sq.  ins. 

(14)  Aggregate  copper  area  =  16-6  x  0-28  =  4-65  sq.  ins. 

(15)  Area  of  one  conductor  =  -^r  =  '0075  sq.  in. 


20 
Current  density  =  Q  QQ7    =  2700    amps,    per 

sq.  in. 

(16)  Length  of  mean  turn  =  2  x  3  '6"  +  STT  -j  =  34" 

(17)  Resistance  of  armature  at  60°  C.  =  0*274  ohm 

(18)  Armature  copper  loss  =  440  watts  approx. 

(19)  Volts  drop  =  11 

These  values  (18)  and  (19)  are  somewhat  higher  than  those  assumed, 
and  may  be  corrected  later. 

1*28  v  106 

(20)  Armature  section  below  teeth  =  Q^-T^T^  -  ~  =  7'5  sq.  in. 

oo,00u  X  ^ 

(21)  Armature  radial  depth  =      sectlon          £«>  „ 

net    length     3-6 

Internal  diameter  of  stamping  =  5-5" 
Weight  of  stampings  neglecting  slots  =  79  Ibs. 
Frequency  =  30 

(25)  Iron  loss  (constant  =  1-8)  =  1-8  x  30  x  0'085  x  79 

=  363  watts. 
Vr  (see  p.  128)  =  2  =  0'38  x  turns  per  section  nearly 

(26)  Turns  per  section  with  4  brush  spindles  =  5  as  a  maximum 

(27)  From  the  particulars  as  outlined,  the  total  armature  losses  will  be 
about  800  watts.     Also,  since  the  maximum  permissible  turns  per  section 
without  interpoles  are  five,  and  these  must  correspond  to  the  highest 
voltage  for  which  the  machine  is  to  be  used  (500),  we  get  an  idea  of  the 
maximum  number  of  slots.     The  number  of  conductors  at  this  voltage 
will  be  about  1  200,  and  it  has  been  shown  that  for  a  two-circuit  winding 
three  coils  per  slot  and  an  odd  number  of  slots  are  convenient  (p.  114). 
Thus   we   conclude   that    about    40   slots   would    be   suitable.      If    the 
machine   be  required  for  500  volts  and   800  r.p.m.,  less  than  37  slots 
would  introduce  difficulties,  and  to  provide  for  lower  speeds  still,  many 
makers  would  adopt  41  slots,  and  some  would  have  two  standard  discs 
with,  say,  37  and  41  slots  respectively.     These  are  matters  for  individual 
judgment,    and   we  shall  assume  that  37  (which   occurs  in  the   list   on 
p.  115)  is  the  number  selected. 

(28)  Commutator.  —  With  the  higher  voltage,  then,  111  sections  will 
be  required.     On  the  lower  voltage  half  this  number  will  suffice,  but  it 
would  hardly  pay  to  stock  two  types  of  segment  for  this  machine,  though 
some  makers  do  so.     Since  about  620  conductors  are  required  for  250 
volts,  we  are  bound  to  choose  either  two  or  three  turns  per  section  with 
111  sections,  and  Vr  is  only  a  limiting  factor  on  the  higher  voltages. 


186     CONTINUOUS   CURRENT   MACHINE   DESIGN 

Thus,  if  0'2  be  the  limiting  thickness  of  one  section  plus  its  insulation, 
the  minimum  diameter  of  the  commutator  is  7",  and  its  peripheral  speed 
is  1350  ft.  per  minute. 

(29)  Commutator  friction  loss  (p.  133)  =  0'00226  x  40  x  1650  x  0-28 

=  42  watts 

(30)  Commutator  resistance  loss  (p.  133)  =  1-2  X  40  X  2  =  96  watts 
Total  138  watts. 

Cylindrical  surface,  allowing  2-|l   __  ^        -ng 
watts  per  sq.  in.  I 

Commutator  length  =  2-|"  axially 

Check  against  Brush  Surface. — With  four  arms,  contact  surface 
per  arm  =  f  sq.  in.  Allowing  brush  -|"  thick  (covers  two  segments)  gives 
axial  length  of  1£"  ;  so  that  the  commutator  dimensions  are  ruled  by 
temperature  rise,  and  2-J"  will  be  sufficient  length,  unless  only  two  brush- 
arms  be  used. 

Division  of  Losses. — We  have — 

Friction  of  bearings,  etc.,  say  2%  (cf.  p.  27)  179  watts 
Commutator  friction            .         .         .         .       42      „ 

Iron  loss  ......  363      ., 

Armature  resistance  loss     .         .          .         .  440      ,, 

Commutator     „  ,,....       96      ,, 

1120      „ 

The  total  losses  are  to  be  (10,400  -  8950)  =  1450 

(31)  So  that  the  shunt  field  loss  will  be  (1450  -  1120)  =  330  watts 

The  constant  losses  then  =914 
The  variable  losses  are  =  536 

.    constant 

Andtheratl°  triable"  = 

The  latter  figure  is  not  specially  good ;  it  is,  however,  a  fair  average 
(cf.  p.  31),  and  may  be  improved  later. 

(32)  Temperature  Rise.     Armature. — The  total  watts  to  be  dis- 
sipated by  the  armature  are  800,  and  we  will  compare   the   probable 
temperature  rise  as  given  by  methods  1,  2,  3,  pp.  81-82. 

Method  1. — Length  of  armature  over  end  connections  =  llf   (p.  84). 
A  =  111"  x  TT  X  11J"  =  406  sq.  ins.  P  =  800 

Now,  although  the  machine  is  small,  the  armature,  being  short  and 
having  a  ventilating  slot,  is  certainly  well  ventilated.  Hence,  we  take 
a  =  40-45,  say  40.  Then  V  =  2720  feet  per  minute,  and  T  =  36°. 

Method  2. — Allowing  for  one  ventilating  space — 
A  =  768,  a  =  85,  P  =  800, 
we  get  T  =  37'5° 

Method  3.— Fig.  47.  The  armature  should  be  capable  of  dissipating 
about  1000  watts ! 


EXAMPLES   OF   PROCEDURE  IN   DESIGN         187 

So  the  average  of  these  calculations  should  prove  that  the  temperature 
rise  will  be  well  on  the  right  side. 

Field. — Watts  to  be  dissipated  per  coil  =  2M  —  82-5. 

If  we  allow  in  Fig.  44,  dc  =  3"  and  r2  =  2J",  and  the  coil  be  supposed 
to  be  taped  and  impregnated,  we  may  take  Ch  as  low  as  180. 

Now,  from  the  equation  on  p.  75 — 

Aw  =  4-7<I0»  +  9-4r2(Zc  +  de)  +  6'28/A 
=  113  +  42-44Zc 

Substituting  this  in  the  heating  equation  (p.  72),  we  get  for  a  mean 
temperature  of  60°  C — 

I,  =  3'2" 

which  is  quite  reasonable,  and  corresponds  to  a  pole  length  of  about  3|". 
First  Approximation  to  Field  Ampere-turns   per  pole  (cf. 
p.  42).- 

Density  at  pole-face  =  45,000 
From  Fig.  13  assume  length  of  gap  0*125". 
Then,  since  pole-arc  =  6'3" 
Distance  between  pole-shoes  =  2*7" 

Ratio  Table  III.  (p.  40)  =  21-6,  and  the  constant  =  3-35 
(33)  Effective  pole-arc  =  6 -7 2"  (actual  value  of  fringing 

factor  =  1-07  instead  of  1*1 
as  assumed) 

Effective  pole-face  area  =  30-4  square  inches 
Density  in  air-gap  if  there  were  no  slots  =  42,000 

Slot  width  =  0-487 

Ratio  ^  in  Fig.  26  =  1 
Ratio  -  in  Fig.  26  =  3-9 

y 

Corresponding  constant  =  1-28 
Actual  air-gap  density  =  42,000  X  1'28  =  54,000 
Air-gap  ampere-turns  =  0-313    X   54,000    X    <H25    =    2100 
Density  at  tops  of  teeth  =  106,000 
Density  at  roots  of  teeth  =  154,000 
Average  density  =  130,000 

(36)  Corresponding  ampere-turns  =  1000  x  0*92  (Fig.  27)  =     920 

(37)  Total  ampere-turns  for  gap  and  teeth  =   3020 

310  x  ^0'5 

(38)  Armature  Cross  Ampere-turns  per  pole  =  -   — -^-  -=  1600 

Ratio  ampere-turns  for  gap  and  teeth 

(39 )  — — • — • — ~~, 1 =  I'oo 

armature  cross  ampere-turns 

If  we  allow  total  ampere-turns  per  pole  =  ampere-turns  for  gap  and 
teeth  X  1*2,  we  see  that  the  former  will  be  about  3600.  A  simple 


1 88     CONTINUOUS   CURRENT   MACHINE   DESIGN 

calculation  on  the  lines  of  that  on  p.  76  shows  that  about  3000  turns  of 
No.  20  S.W.Cr.  will  easily  go  into  the  space  calculated  from  temperature 
rise,  and  will  provide  the  3600  ampere-turns  when  expending  the  required 
watts  at  the  specified  pressure. 

(40)  Approximate  Weights  and  Costs  of  Effective 
Material.— 

£ 

Armature— Iron,  80  Ibs.  @  5d.        .     ;    .         .       1-67 

Copper,  24  Ibs.  @  I/-    .         .         .       1-20 

Magnets— Poles  and  shoes,  steel,  68  Ibs.  @  1  \d.     0-43 

Yoke,  cast  iron,  420  Ibs.  @  Id.     .       1'75 

Coils,  90  Ibs.  @  lOd.    .         .         .       3-75 

Commutator — 25  Ibs.  copper  @  I/-     .       '.    *     .       1-25 

£10-00 

If  we  assume  that  the  ratio  of  total  works  cost  to  cost  of  effective 
material  is  for  this  size  3~,  the  total  works  cost  of  this  machine  would  be 
about  £35.  The  present  (1909)  selling  price  is  less  than  £40,  so  that  the 
margin  is  too  small. 

Criticisms  of  First  Design. — The  preceding  paragraph  shows  that 
the  cost  of  the  machine  is  too  high,  and  we  shall  now  indicate  a  method 
of  arriving  at  a  better  result.  It  is  evident  that  we  must  either  (1)  de- 
crease the  cost  of  production  or  (2)  increase  the  output  for  the  material 
used. 

Alterations  to  Reduce  the  Cost. — The  heaviest  item  in  the 
table  of  costs  is  the  field  magnet  copper.  This,  however,  cannot  be 
reduced  without  either  a  corresponding  reduction  in  the  field  ampere- 
turns,  or  an  increased  field-loss.  The  former  is  the  only  practicable  course. 

The  ratio  (39)  is  1'88,  but  according  to  p.  124  it  need  not  much 
exceed  1*3. 

The  cheapest  way  of  reducing  the  field  ampere-turns  is  by  shortening 
the  air-gap  ;  thus,  with  an  air-gap  of  — "  instead  of  |"  the  gap-density, 
after  allowing  for  the  various  correction  factors,  becomes  about  55,000,  the 
ampere-turns  for  gap  and  teeth  become  2540,  and  the  total  ampere-turns 
per  coil  become  3100.  Now,  equations  worked  out  like  those  on  p.  76 
show  that  a  coil  smaller  than  that  already  arranged  will  hardly  dissipate 
82-5  watts. 

Three  courses  are  open — 

(a)  Reduce  field  lost  watts  and  increase  armature  lost  watts. 

(b)  Use  a  ventilated  field-coil. 

(c)  Change  the  pole-shape  and  get  a  larger  cooling  surface.* 

All  these  alternatives  could  be  tried ;  we  prefer  the  first,  especially 
as  the  armature  will  (from  the  temperature  calculations)  dissipate  rather 

*  It  should  be  observed  that  this  very  difficulty  not  infrequently  favours  the  use 
of  a  field-pole  of  rectangular  section,  besides  the  fact  that  a  round  coil  leads  to  a 
yoke  of  rather  larger  diameter  for  a  given  flux. 


EXAMPLES   OF   PROCEDURE   IN   DESIGN         189 

more  than  is  at  present  required  of  it.  Thus  with  field-coil  depth  of  2", 
3100  turns  per  coil  of  No.  21  will,  with  afield-current  of  one  ampere,  give 
the  required  ampere-turns,  with  a  loss  of  62  watts  per  coil. 

To  maintain  the  same  efficiency,  then,  the  armature  must  now  dissipate 
522  watts  due  to  resistance,  and  363  due  to  iron  ;  total  885.  This  it  will 
apparently  do,  as  new  temperature  calculations  show. 

The  armature  current  thus  becomes  43 '6  amperes,  and  field-current 
one  ampere.  Thus — 

Total  input  =  44-6  x  250  =  11180  watts 

Field  loss  =  250 

Armature  loss  =  885 

Commutator  loss  =  138 

Bearings,  etc.  =  179 


Total         .         .         .     1452  watts 

Output     .         .         .     9728  watts  =  13  H.P. 

Efficiency  =  87% 

The  ratio  ampere-turns  for  gap  and  teeth  -f-  cross  ampere-turns  of  the 
armature  becomes  fffg  =  T49,  which  is  a  great  improvement  on  the  previous 
design ;  and  the  cost  of  net  effective  material  is  reduced  from  £10  to 
£9-25 ;  so  that  with  the  same  ratio  as  recently  used  the  total  works  cost 
becomes  ,£32'  4,  leaving  a  rather  better  margin  considering  that  the 
horse-power  is  now  raised. 

Without  going  into  the  cost  of  non-effective  parts,  such  as  end- 
plates,  bearings,  etc.  (to  do  which  requires  a  full  knowledge  of  the 
particular  works),  this  result  is  about  the  best  that  can  be  obtained  for 
a  design  (without  interpoles),  which  has  to  be  adapted  for  500  volts. 
It  should  be  noticed  that  it  is  the  latter  condition  which,  by  limiting  the 
turns  per  section,  prevents  a  greater  output  from  being  obtained.  This 
machine,  however,  should  not  be  proceeded  with  until  one  or  two  ratios 

Y 
of  ^  have  been  similarly  worked  through.     We  shall  assume  that  this 

has  been  done,  and  that  a  general  comparison  of  the  results  is  in  favour 
of  the  11J"  armature,  so  that  we  may  pass  to  the  calculation  of  the  final 
details. 

Armature  Turns  and  Voltage. — With  the  number  of  commutator 
sections  selected  we  have  choice  of  the  following  numbers  of  armature 
conductors,  using  a  two  circuit  winding  : — 

Turns  per  Armature  Volts 

section.  conductors.  generated.  Speed. 

1  .  .  222  .  .  100  .  .  1060 

2  .  .  444  200  .  .  1060 

3  .  .  666  .  .  240  .  •_.  848 

4  .  .  888  .  .  400  1060 

5  1110  480  1010 


190    CONTINUOUS   CURRENT   MACHINE   DESIGN 

All  of  which  are  useful   speeds  and  voltages  ;  with  lower  speeds  easily 
obtainable  thus — 

5         .'..;'•      1110         .         .         240         .         ,         500 

Evidently  the  most  serviceable  armatures  will  be  those  having  3,  4, 
and  5  turns  per  section. 

Arrangement  of  Slot. — Recalculating,  we  have — 

Equivalent  pole-arc  =  6 "65" 
Teeth  per  pole  =  6*8 

Width  of  tooth  root  (with  a  maximum  density  =  154,000)  =  0-338" 
From  these  it  is  an  easy  step  to  the  equation — 

Slot-depth  =  3-75"  -  5'9  x  width  of  slot 
Whence  the  following  table  giving  possible  useful  slot  dimensions  :  — 

TABLE  XXII. 

Slot-width.  Slot-depth.  Tooth-width  at  periphery. 

0^375"  .  .  .  1-54"  ...  0-6 

0-4"  .  .  .  1-4"  .         .         .  0-575 

0-4375"  .  .  .  1-16"  .         .         .  0-5375 

0-45"  .  .  .  1-1"  .         .         .  0-515 

0-46875"  ...  1"  ....  0-506 

0-4875"  .  .  .  0-87"  .         .         .  0-4875 

It  will  be  noted  that  the  figure  given  by  the  approximate  formula 
(p.  184)  is  very  near. 

Arrangement  of  Conductors  in  Slot. — The  most  generally  useful 
arrangement  is  that  of  Fig.  87  ;  but  it  is  evident  that  if  round  wire  be 
adopted  the  same  depth  and  width  cannot  be  convenient  for  3,  4,  and  5 
turns.  This  leads  makers  to  select,  and  sometimes  stock,  more  than  one 
slot-shape  for  a  given  armature.  If  we  keep  as  near  as  possible  to  our 
original  design  by  adopting  for  this  calculation  666  armature  conductors, 
we  must  arrange  the  slot  for  three  turns  per  section,  18  conductors  per 
slot.  Allowing  the  slot-linings  given  in  Table  IX.,  p.  144,  with  7  mils  of 
tape  round  each  individual  group  of  wires,  and  7  mils  of  tape  round  each 
group  of  coils,  we  have — 

Total  thickness  of  insulation  excluding  wire-covering  =  0'116" 
Similarly — 

Total  depth  of  insulation  exclusive  of  cotton  covering      0*086 
Separator  between  upper  and  lower  coils     .         .         .     0*03 
Binding  wire  space      .......     0'060 


Total    .         .  .     0-176 

Now,  the  wires  themselves  evidently  require  a  space  proportioned  three 
wide  by  six  deep ;  i.e.  2:1. 

The  problem  then  is  to  choose  that  slot  which  minus  0-104"  in  width 


EXAMPLES   OF   PROCEDURE   IN   DESIGN         191 

and  0*17"  in  depth  has  a  ratio  depth  to  width  of  2  to  1.  In  this  way  is 
the  most  economical  shape  of  slot,  in  the  case  of  wire-wound  armatures, 
subservient  to  practical  limitations.  For  these  conditions  the  best  slot 
is  0*48"  X  0-92".  For  a  4-turn  armature  with  appropriate  insulation  a 
slot  T7/  (=  0-4375)  x  1-16"  would  be  better. 

For  a  5-turn  armature  also  the  latter  proportions  are  better,  so  that 
possibly  this  slot  might  be  chosen  as  the  standard.  If  we  assume  that 
this  is  done,  then  the  largest  wire  that  can  be  got  in  with  250-\olt 
insulation  is  No.  13  S.W.G.,  and  that  only  with  special  fine  covering. 
With  the  wider,  shallower  slot  No.  1 2  would  go  in  easily  with  special  fine 
covering,  or  No.  13  very  easily.  No.  13  S.W.G.  gives  in  the  former 
case  a  space-factor  of  0'24,  and  in  the  latter  case  0*28. 

Other  points  affecting  the  final  choice  of  slot-dimensions  are  the 
standard  slot-stamping  tools  available,  as  well  as  the  number  of  machines 
requiring  5-turn  armatures  as  compared  with  those  requiring  3 -turn 
armatures ;  and  the  possibility  of  adopting  two  small  wires  in  parallel 
instead  of  one  large  one  in  the  5-turn  case.  The  latter  has  the  effect  of 
considerably  modifying  the  slot-dimensions,  but  it  will  not  be  found  very 
convenient  in  this  instance.  Another  adjustable  coefficient  is  the  ratio 
of  nett  to  gross  armature-length.  This  we  have  taken  at  0'8,  and  a 
simple  calculation  shows  that  this  will  allow  of  a  ventilating  space  0*4" 
wide.  This  latter  might  be  reduced  to  0'375"  or  slightly  less,  and  thus 
allow  of  a  wider  slot  with  the  same  tooth-density.  It  should  also  be  remem- 
bered that  where  round  wires  only  are  likely  to  be  used,  as  in  the  present 
example,  the  bottom  corners  of  the  slots  can  be  slightly  rounded,  say  with 
a  radius  of  ~",  and  that  then  the  slot  can  be  deepened  by  the  amount 
of  this  radius  without  increasing  the  tooth-root  density.  So  that  perhaps  on 
the  whole,  if  only  one  size  of  slot  is  to  be  standardized,  a  width  of  0'45" 
and  a  depth  of  1J"  with  a  3^"  corner  radius  is  the  best  solution.  This 
allows  of  a  wire  for  the  3-turn  armature  0*096"  diameter  with  ordinary 
D.C.C.,  while  the  4-turn  armature  will  have  a  wire  equivalent  to  No.  13 
D.C.C.,  and  the  5-turn  armature  may  be  wound  with  No.  14  or  15  D.C.C. 
according  to  the  voltage. 

Thus  for  the  3-turn  armature  we  have — 

Slot  depth.— Six:  wires  (each  O'llO  when  covered)  0*660 

Various  tapes       ....         .  .  0-056 

Binding  wire,  etc.         .         .         .  .  0-062 

Slot  lining   .         ...         .  .  .  0-030 

Separator  and  making-up  pieces    .  .  0'317 


1-125 

Slot-width.— Three  wires  .  .  .  .  .  .  0-330 

Tapes  .         .  .-...'  .  ;  .  .  0-056 

Lining         - .  •  .  .  ,  .  .  0-060 

Allowance    .  .  .  .  ,  .  0-004 

0-450 


1 92     CONTINUOUS   CURRENT   MACHINE   DESIGN 

The  slot  is  of  course  wasteful  in  depth,  and  the  space-factor  is  only 
0*27.     It  has  been  sacrificed  to  standardization. 
In  the  five-turn  armature  we  have — 

Slot-height.— Tea  No.  14  D.C.C.        .  .  .  .     0-920 

Tapes           .         .         .  .  .  .     0-056 

Binding  wire,  etc.         . '  .  .  .     0'062 

Slot-lining    .     —7--     .  .  .  .     0-050 

Separator     .         .     ^\  .  .  .0-037 

1-125 

Slot-width.— Three  No.  14/s.    .         .      I   .         .         .  0-276 

Tapes  .         .         .     /   .         .         .  0-056 

Lining 0-100 

Allowance  .  0*018 


0-450 
Space  factor  =  0'29 

The  last  figure  is  very  good,  but  the  slot  is  somewhat  crowded  for  a 
high  voltage.  The  "  allowances  "  are  for  spring  of  the  wire  and  variations 
in  the  insulation  thickness. 

These  examples  should  suifice  to  illustrate  the  method  of  determining 
convenient  slot  proportions.  It  will  be  noticed  that  while  theoretical  ratios 
have  little  to  do  with  the  final  determination,  yet  this  latter  is  very  near 
the  preliminary  figures  under  (13),  (14),  (15)  above,  as  can  easily  be  seen 
by  placing  the  various  results  side  by  side. 

General  Conclusion. — The  machine  is  now  known  to  be  satisfactory 
in  all  its  important  points,  viz. — 

Cost,  ampere-turns  of  armature  and  of  field,  reactance-voltage, 
efficiency,  constant  losses,  variable  losses,  temperature-rise,  flexibility  of 
output. 

Final  Calculations. — The  following  details  should  be  finally 
calculated. 

1.  Ampere-turns  per  pole  as  carried  out  on  pp.  41  and  56. 

2.  Length  of  armature  winding  as  on  p.  163. 

3.  Armature  winding-pitch  as  on  p.  114. 

4.  Commutator  pitch  as  on  p.  114. 

5.  Final  iron  losses  from  curves  such  as  Fig.  16. 

6.  Temperature  rise  and  output  for  the  four-  and  five-turn  armatures. 

7.  Commutator  lengths  for  different  voltages. 

8.  Actual  back  E.M.F.  and  speed  for  different  armature-windings. 
Range  of  Outputs. — The  slot  having  been  arranged  to  accommodate 

3,  4,  and  5  turns  per  section,  it  is  desirable  to  tabulate  the  range  of  out- 
puts obtainable.  As  on  the  five-turn  armature  the  space-factor  is  good, 
there  will  be  little  object  in  varying  the  armature  length,  and  the  com- 
parison suggested  may  be  carried  out  by  filling  in  a  table  like  that  given 
below,  remembering  that  a  two-circuit  winding  may  be  also  connected  as 
multiple-circuit. 


EXAMPLES   OF   PROCEDURE   IN   DESIGN         193 


TABLE  XXIII. 

DESIGN  No.  .  FLUX  PER  POLE  IN  THE  ARMATURE,  1'28  x  108  LINES; 
D  =  11J",  L  _  4j"  .  COMMUTATOR  DIAMETER  7";  SECTIONS  111 ; 
ARMATURE  SLOTS  37. 


Turns 
per 
section. 

Amps. 

Volts. 

Speed. 

H.P. 

React- 
ance 
volts, 

Armature. 

Field 
loss. 

Commu- 
tator. 

C2R 

Iron  loss. 

C2R 

Fric- 

r. 

tion. 

3 

44-6 

250 

840 

13 

1-14 

520 

365 

250 

96 

42 

3 

46-2 

220 

740 

12 

1-14 

560 

320 

250 

4 

250 

4 

440 

4 

500 

5 

250 

5 

440 

5 

500 

From  a  series  of  tables  like  this  it  is  possible  to  deduce  the  next  most 
convenient  size  of  machine  which  would  then  be  proceeded  with.  In 
working  out  the  list,  however,  one  finds  oneself  repeatedly  prevented 
from  using  the  carcase  for  outputs  which  might  be  of  use  because  of  the 
reactance  voltage  limit,  and  thus  one  is  led  naturally  to  consider  means 
for  obviating  this  disadvantage.  When  making  up  the  costs  of  the  com- 
plete machine,  also,  one  finds  that  the  non-effective  material,  which  in  a 
machine  of  this  size  will  cost  about  ,£7,  will  be  about  the  same  so  long  as 
the  armature-diameter  remains  constant,  whatever  its  length ;  so  that  one 
naturally  inclines  toward  lengthening  the  armature  to  increase  the  output ; 
but  here  again  reactance  voltage  and  field-copper  cost  intervene. 

To  a  certain  extent  the  latter  is  compensated  for  by  the  relatively 
reduced  cost  of  non-effective  material,  and  by  the  fact  that  a  greater  per- 
centage of  armature  copper  is  rendered  effective  ;  so  that  up  to  the  point 
where  these  conflicting  conditions  balance,  the  increased  length  of  arma- 
ture is  undoubtedly  an  advantage. 

This  reasoning  all  tends  toward  the  adoption  of  means  for  compensating 
armature-reaction  and  reactance-voltage,  and  the  only  cheap  and  effective 
possibility  is  the  interpole. 

Interpoles. — The  justification  for  the  use  of  interpoles  in  small 
machines  not  specially  intended  for  wide  speed  variation  is,  then,  that 
(a)  being  independent  of  reactance-voltage  and  of  armature-reaction,  the 
armature  may  be  lengthened  and  the  air-gap  shortened  until  the  reduced 
field -copper  due  to  the  latter,  and  the  relatively  reduced  cost  of  end  plates, 
etc.,  show  a  substantial  advantage  over  the  increased  L.M.T.  of  the  field, 
the  cost  of  the  interpoles,  and  the  increased  armature  material ;  so  that 
at  the  increased  output  obtained  the  cost  per  K. "W.  is  substantially  reduced. 

O 


194    CONTINUOUS   CURRENT   MACHINE   DESIGN 

Application  to  I3-H.P.  Motor. — In  the  present  instance  the 
procedure  might  be  somewhat  as  follows  : — 

Few  makers  would  care  to  reduce  the  air-gap,  though  in  the  author's 
opinion  this  might  safely  be  made  -j~",  thus  saving  600  ampere-turns  per 
shunt  field-coil. 

The  present  cost  of  net  effective  material  is  £0-71  per  H.P.,  or  adding 
£7  for  non-effective  material,  we  get  £1-25  per  H.P. 

The  amount  by  which  the  armature  can  be  economically  lengthened 
is  largely  a  matter  of  trial  and  error,  and  we  may  commence  by  trying  an 
increased  gross  length  of  50  per  cent.  The  poles  must  now  be  made 
elliptical  or  rectangular  in  section.  Adopting  the  latter,  we  get — 

L  =  4-5  x  1-5  =  6-75 
Flux  per  pole  in  the  armature  12*8  x  105  X  1-5  =  19-2  x  105 

If  one  air-duct  through  the  armature  be  still  used,  the  new  net  length 
becomes — 

(6-75  -  0-4)  x  0-9  =  5-7" 
Ratio  net  length  :  gross  length  =  0*84 

So  that  the  densities  in  teeth  and  armature  are  reduced  almost  in  the 
proportion  0'8  :  0'84.  Whence,  as  a  first  approximation,  the  ampere- 
turns  for  gap  and  teeth  become  2000,  and  the  total  shunt  ampere-turns 
per  pole  are  2400  (cf.  p.  187). 

*(2)  Pole-area  =  16  X  1-5  =  24  sq.  in. 
(6)          Pole  axial  length  =  6-75" 
Pole-thickness  =  3-55" 

(32)  Allowing  the  same  shunt  current  as  before  (viz.  1  ampere),  we 
find  that  about  2400  turns  per  coil  of  the  same-sized  wire  (No.  20  S.W.G.) 
will,  in  a  coil  3J"  long  x  If"  deep  dissipate  the  heat  readily,  and  require 
about  30  Ibs.  of  copper  per  coil.  The  rectangular  coil  acounts  for  this 
increase  in  copper  for  the  same  loss,  the  L.M.T.  being  nearly  30".  The 
same  pole-length  will  therefore  be  used,  and  the  diameter  of  yoke  will 
remain  the  same,  its  section,  and  therefore  its  weight,  being  increased  by 
50  per  cent,  to  maintain  the  density  constant. 

Armature  Output. — At  840  r.p.m.,  with  three  turns  per  section  and 
19-2  x  105  lines  per  pole,  the  generated  back  E.M.F.  will  be  358  volts. 
L.M.T.  of  armature  becomes  38£". 

(17)  Ra  =  0-31  ohm. 

(31)  Temperature  rise  calculations  show  that  the  armature  will 
dissipate  about  1200  watts. 

'23)          Weight  of  stampings  neglecting  slots  =  115  Ibs.  approx. 
24)  Frequency  =  28 

(25)  Iron  loss  =  486  watts 

(18)  Copper  loss  in  armature  =  (1200  -  486)  =  714  watts 

Maximum  armature  current  =  at  least  50  amps. 
Output  =  358  x  50  =  about  24  H.P. 

*  The  reference  numbers  apply  to  the  previous  calculation. 


EXAMPLES   OF   PROCEDURE   IN   DESIGN         195 

Output  of  the  Five-turn  Armature.  —  A  simple  calculation  shows 
that  at  a  speed  of  about  800  r.p.m.  the  machine  will  give,  on  500  volts 
with  five  turns  per  section,  about  18  H.P.  This  corresponds  to  about 
2000  armature  ampere-turns  per  pole  and  a  reactance-voltage  Vr  =  2-5. 
Both  these  show  the  necessity  for  interpoles.  Evidently  to  neutralize 
armature  reaction  alone,  each  interpole  must  carry  2000  ampere-turns. 
Besides  this  we  must  set  up  the  commutation  flux. 

Recalculating  the  five-turn  armature  of  p.  192,  we  obtain:  length  of 
mean  armature  turn  =  38J". 

(17)  Armature  resistance,  0'84  ohm;  resistance  of  one  armature  coil, 
0-03  ohm. 

Calculating  the  value  of  /as  on  p.  123,  we  get  /  =  1020  if  the  maximum 
number  of  turns  short  circuited  =  3.  This  corresponds  to  a  brush  J"  wide. 

From  this  we  obtain  Lc  =  0-000255 
also  with  a  brush  J"  wide  tc  —  -^—  seconds 


whence     -*  =  0-23 


From  Fig.  80  € 

Since  Cw  =  15  '5,  we  have 


'  =  0'8 


e  =  4  volts 


Substituting  this  in  the  formula  on  p.  123,  we  get — 
Interpole  flux  =  8  x  104  lines  per  pole 

As  a  first  approximation  take  the  leakage  factor  for  the  interpole  itself 
as  1'8,  and  allow  a  density  of  say  100,000  lines  in  the  pole,  then  the 
diameter  of  the  interpole  is  say  I-—. 

The  ratio  of  the  interpole-arc  to  the  armature 
circumference  should  be  at  least  as  great  as  that  of 
the  brush  width  to  the  commutator- circumference, 
so  that  the  coil  may  be  under  the  interpole  shoe 
during  the  whole  time  of  commutation. 

In  this  case  the  pole-arc  may  be  1",  so  that 
the  pole  will  slightly  overhang  the  shoe,  but  this 
is  of  no  consequence. 

Taking  a  density  under  the  shoe  of  40,000  lines 
per  square  inch  gives  us  an  axial  length  of  shoe 
of  about  2  inches.  The  pole,  therefore,  is  formed 
much  as  in  Fig.  123,  but  the  neighbouring  pole- 
shoe  is  not  cut  away.  The  interpole  air-gap  may 
be  the  same  as  the  gap  under  the  main  poles,  i.e. 
~",  and  the  ampere-turns  may  be  calculated  exactly 
as  for  the  main  poles. 

We  thus  find  the  ampere-turns  for  the  air-gap  =  1174,  and  allowing 
12  per  cent,  extra  for  the  iron  path  gives  1408  ampere-turns  for  the 
interpole,  or  say  1400. 


196     CONTINUOUS   CURRENT   MACHINE   DESIGN 

The  armature  cross-ampere-turns  are  2000,  so  that  the  total  ampere 
turns  per  interpole  =  3400. 

Full-load  current  =31  amps 
Turns  per  coil  =  S|°o  =  110 

Interpole  Loss. — A  rough  calculation  of  the  efficiency  shows  that  in 
this  case  we  can  afford  to  take  the  loss  at  1  per  cent,  or  140  watts. 

As  the  interpole-coils  will  not  be  taped,  and  because  they  are  not 
deep,  Gh  may  be  taken  at  about  150. 

Carrying  out  the  calculation  for  temperature  rise  exactly  as  for  shunt 
field  coils,  we  find  that  110  turns  per  pole  of  No.  7  S.W.G.  D.C.C.  will  give  a 
loss  of  about  130  watts  and  a  temperature  rise  of  about  55°  Centigrade  mean. 

Losses  and  Efficiency. — Checking  out  now  the  losses  and 
efficiency,  we  get — 

Armature  input  =  31  x  500  =  15,500 
Field  loss  =       250 


Total  input  .         .     15,750  watts 

Armature  copper  loss  =  814 

Iron  loss  =  386 

Shunt  field  =  250 

Com.  losses  and  friction  =  320 

Interpole  loss  =  140 

Total  losses  .         .       1,910 

Output          .         .     13,840=  18J  H.  P. 
Efficiency  =  88%,  which  agrees  well  with  Fig.  19. 
Possibility  of  enclosing. — 

Total  variable  losses  including  interpoles  =  1050 

Total  constant  losses  =  860 
Ratio  constant :  variable  losses  =  0*815 

This  is  a  great  improvement  on  the  non-interpole  machine,  where  the 
ratio  was  1-7  (see  p.  186).  The  result  of  this  low  ratio  is  that  the 
machine  will  have  its  maximum  efficiency  at  a  load  less  than  full  load, 
and  it  will  be  almost  as  good  enclosed  as  when  open. 

Effect  on  costs. — The  costs  for  this  machine  come  out  about  as 
follows  : — 

£ 

Armature  iron .         .         .         .         .         .         .1*9 

Armature  copper 1  '36 

Steel  poles        .         .         .                  .         .         .  0'64 

Iron  yoke 2-62 

Shunt  field-coils 3 -93 

Commutator  (not  shortened  for  500  volts)         .  1*25 

Interpole  coils  .         .         .                   .         .         .  1*3 

Total  cost  of  effective  material  .  13-00 


198     CONTINUOUS   CURRENT   MACHINE   DESIGN 

If  the  cost  of  non-effective  material  be  again  taken  at  £7,  we  have  a 
total  material  cost  of  .£20,  or,  at  a  speed  of  840,  £0-83  per  H.P.  as  against 
£1'26  per  H.P.,  which  was  the  best  obtainable  without  interpoles. 

If  we  take  the  ratio  of  total  works  cost  to  cost  of  net  effective  material 
as  3*25,  the  total  works  cost  becomes  £42,  and  the  selling  price  to-day 
(1910)  is  about  £52.  So  that  the  addition  of  the  interpoles  has  reduced 
the  specific  cost  without  sacrificing  the  efficiency. 

Final  calculations. — It  is  to  be  noted  that  although  this  last 
machine  may  be  taken  as  a  fair  example  of  modern  practice,  the  designer 
should  not  rest  satisfied  with  it  until  he  has  assured  himself  that  it  is  the 
best  that  can  be  done.  Further,  it  is  seen  that  the  best  shape  of  machine 
without  interpoles  is  different  from  the  best  shape  with  interpoles,  so  that 
to  take  a  standard  machine  and  add  interpoles  is  a  mistake. 

The  use  of  ball  bearings  in  small  machines  is  coming  into  favour,  as 
it  raises  the  efficiency  considerably,  because  it  halves  the  friction  loss  and 
thus  saves  a  certain  amount  of  heat  which  would  otherwise  have  to  be 
dissipated. 

Of  course,  before  any  machine  is  put  in  hand  all  the  figures  should  be 
most  carefully  rechecked,  especially  as  regards  temperature  rise,  upon 
which  an  interpole  design  entirely  depends.  The  author  thinks  that 
with  carefully  arranged  ventilation  or  by  the  use  of  a  fan  mounted  on  the 
armature  shaft  (Fig.  124),  even  the  figures  above  obtained  could  be  still 
improved  by  5  or  10  per  cent.  Possibly  a  slightly  lower  tooth  density 
and  longer  air-gap  would  be  preferred  by  many  makers. 


CONSTANT  PRESSURE  MACHINES. 
Problem  II. 

As  a  further  example  of  constant-speed  machines  we  will  consider  the 
main  dimensions  of  a  200-jK".TT.  generator  with  interpoles  to  run  at  400 
r.p.m.  This  example  will  be  the  more  interesting  since  we  have  already 
made  use  of  a  machine  of  this  output  without  interpoles  to  exemplify 
formulae  and  statements  in  various  chapters. 

We  have  thus  obtained — 

From  the  commutation  limit  (p.  132),  D  =  35"  for  circular  poles 
With  4  poles  L  =  15"         D2L  =  18,500 
With  6  poles  L  =  10"         D2L  =  12,200 
With  8  poles  L  =  7J"         D2L  =  9100 

The  latter  figure  agrees  with  those  obtained  from  temperature  con- 
siderations on  pp.  28  and  85,  assuming  that  with  8  poles  the  division  of 
losses  and  efficiency  was  still  about  the  same  as  for  the  4-pole  case ;  so 
that  the  number  of  poles  in  non-interpole  machines  is  often  determined 
by  the  problem  of  getting  the  dimensions  demanded  by  commutation  to 
coincide  with  those  required  by  temperature-rise. 

Type   of  Armature   Winding. — The   question  of    the    type   of 


EXAMPLES   OF   PROCEDURE  IN   DESIGN          199 

armature-winding  has  some  effect  upon  the  number  of  poles.  In  non- 
interpole  machines  of  this  size  two-circuit  windings  are  usually  very 
unsatisfactory,  and  for  500  volts  a  multiple-circuit  winding  is  out  of  the 
question  with  8  poles,  on  account  of  the  large  number  of  conductors 
required.  Interpole  machines,  on  the  other  hand,  can  be  arranged  with 
a  two-circuit  winding  for  almost  any  output.  This  also  affects  the  space 
factor.  For  the  fewer  bars  per  slot  required  by  a  two-circuit  armature 
render  a  higher  space  factor  possible  (see  p.  146). 

Deductions  from  Standard  Makers.  —  It  is  evident  that  the 
question  of  the  number  of  poles  to  be  used  is  one  of  the  difficult  points  to 
decide  in  such  a  case  as  this.  If,  as  in  Problem  I.,  we  compare  some 
similar-sized  machines  of  different  makers  this  is  further  emphasized. 
For  instance,  take  the  two  following  interpole  machines  by  first-class 
makers  :  — 


A  B 

Output  K.W.         .         .          200  .         .  200 

Volts     ....          500  ..  500 

Speed  r.p.m.  ...          400  ..  400 

Poles                       .         :~~          8  4 

D  (inches)     ...            34J  .  27J 

L  (inches)      ...            lOf  .  13 

D2L       .                               12,500  .         .  9850 

Peripheral  speed   .         .        3600  .         .  2900 

ratiopole-arc                           0<75  0.7 
pole-pitch 

....          400  ..  750 


Here  it  is  apparent  that  for  machines  of  similar  output  the  two 
makers  have  decided  upon  very  different  designs.  From  the  point  of 
view  of  active  material  alone  B  would  probably  be  dearer  than  A  ;  but 
the  smaller  amount  of  inactive  material  in  B  (due  to  the  smaller  diameter) 
might  possibly  compensate  for  this.  It  will  be  noticed  that  the  value  of 
Y 
-^  in  the  former  case  agrees  with  the  limits  mentioned  on  p.  62,  but 

the  latter  is  far  higher. 

Assumed  Densities,  etc.  —  Since  this  design  is  to  be  fitted  with 
interpoles,  we  may  choose  the  tooth-densities  and  gap-length  rather  lower 
than  otherwise  would  be  permissible.  We  take  — 

Material  of  yoke  and  poles         .  cast  steel 

Poles          .....  circular 

Shoes         .....  laminated 

Air-gap  (Fig.  13)       ...  0-125" 

Voltage     .....  500 

Winding   .....  two-circuit 


200     CONTINUOUS   CURRENT   MACHINE   DESIGN 

Slot  space-factor        .         .         .  0'38 

Temperature  rise  on  full  load    .  40°  C. 

Efficiency  .         .         .         .  93%  to  be  a  maximum  at  f  full  load 

Density  at  the  pole-shoe  face     .  50,000 

Maximum  tooth-density     .         .  140,000 

Density  below  teeth          .         .  75,000 
A               .                  .         .         .1*15  (assumed) 

Yoke-density    ....  80,000 

Pole-density      ....  100,000 
Pole-arc  7 

pole-pitch 

Total  generated  E.M.F. — The  total  copper-loss  in  armature  and 
in  terpoles  will  probably  not  exceed  3  percent,  of  the  output.  If,  then,  we 
reckon  on  a  maximum  flux  corresponding  to  520  volts,  we  ought  to  be  on 
the  safe  side. 

Relationship  of  D  and  L. — From  the  densities  above  given  and  in 
accordance  with  the  analysis  on  p.  20,  we  obtain — 


"1-61 

Depth  of  Slot. — Substituting  in  the  formula  on  p.  15,  we  get — 
Depth  of  slot  =  0-05D 

Important  Ratios. — These  are  the  same  as  in  the  previous  example 
(p.  183),  except  that  Vr  is  of  little  importance  since  the  machine  has  inter- 
poles. 

Value  of  ^.— We  have— 


C 

and  X  =  iv  ^ 

A 

But  w  =—2        (neglecting  X) 


,  Y    dy 

whence  =  J      approximately 


Y 

Selecting  now  a  trial  value  for  ^  in  accordance  with  p.  62 

Say  ^  =  400 

We  get  d2p  =  440 

whence  if  L  =  d,  we  obtain  the  following  table  for  likely  numbers  of 
poles  :  — 


EXAMPLES   OF   PROCEDURE  IN   DESIGN 


201 


TABLE  XXIV. 


Poles. 

D. 

L. 

D2L. 

Peripheral  speed. 

4 

26" 

10-5" 

7,100 

2720 

6 

32" 

8-6" 

8,800 

3300 

8 

37" 

7-5" 

10,200 

3840 

It  is  evident  that  the  problem  of  the  right  number  of  poles  to  adopt  is  the 
first  that  arises  in  a  machine  of  this  size. 

The  choice  of  the  above  possible  machines  must  be  decided  from  a 
consideration  of  temperature-rise  and  cost.  We  therefore  proceed  to 
analyze  the  division  of  losses  for  the  three  cases. 

Losses. — Since  the  efficiency  is  to  be  93  per  cent,  at  J  load,  we  obtain 
from  p.  85 — 


Constant  losses 
Variable  losses 

We  further  assume,  as  on  p.  30  — 

Friction  of  bearings  and  windage 


5250  watts 
9300 


1200  watts 


To   obtain   an   approximation   to   the    iron   losses,    we    tabulate    as 
follows  : — 

TABLE  XXV. 


Design  No. 

I. 

II. 

III. 

Poles           

4 

6 

8 

D       

26" 

32" 

37" 

d        

10-5" 

8-6" 

7-5 

Flux  in  pole        .... 

86-5  x  105 

58  x  105 

44  x  105 

Slot-depth  

1-3" 

1-6" 

1-85" 

Flux  in  armature 

75  x  105 

50  x  105 

38-2  x  105 

Section  below  teeth    . 

50 

33 

25-5 

Net  length          .... 

8-4" 

7" 

6" 

Radial  iron  depth  including  slot 

7-3" 

6-5" 

6-1" 

Volume  of  core  neglecting  slots  . 

3630 

3680 

4040 

Weight,  Ibs  

1010 

1050 

1130 

Frequency  ..... 

13-3 

20 

26-6 

Constant  (p.  29) 

1-7 

1-7 

1-7 

Iron  loss     ..... 

1720 

2700 

3850 

202     CONTINUOUS   CURRENT   MACHINE   DESIGN 

Variable  Losses. — With  interpoles  a  comparatively  soft  brush  may 
be  used,  as,  say,  Battersea  B  type  with  a  voltage  drop  at  the  commutator 
of  1.  Thus  the  commutator  copper  loss  is  2  x  400  =  800  watts,  and  .the 
interpole  loss  may  be  taken  provisionally  at  0*3  per  cent.,  i.e.  600  watts 
(see  p.  124).  Subtracting  these  items  from  9300  gives  an  armature 
copper  loss  of  7900  watts.  Adding  this  to  the  iron  losses  just  calculated, 
we  obtain — 


TABLE  XXVI. 


Design  number. 

I. 

II. 

III. 

Total  watts  armature  must  dissipate 

9,620 

10,600 

11,750 

Method  2,  p.  82  J^  =     ' 

56 
56° 

52 

46° 

50 

42° 

Watts     armature     will      dissipate,! 
Method  3,  p.  82  .         .         .         .( 

7,200 

9,500 

10,400 

Length  of  mean  armature-turn 

79" 

63" 

55" 

Armature  conductors 

520 

520 

510 

Aggregate  slot  area 

53 

80 

107 

Net  copper  area       .         .         . 

20-5 

30-4 

40-6 

Area  per  conductor 

0-042 

0-064 

0-086 

Armature  resistance  loss  at  55° 

15,100 

7,800 

5,100 

Comparing  the  last  figures  with  the  copper  loss  calculated  from  the 
efficiency  (viz.  7900  watts),  and  noting  the  inferences  to  be  drawn  from 
the  temperature  rise  figures,  we  see  that  the  four-pole  design  is  out  of  the 
question.  Either  the  six-  or  eight-pole  machine  will,  with  slight  modifi- 
cations, evidently  yield  the  output,  and  both  should  be  worked  through. 
On  account  of  its  much  smaller  diameter  and  iron  loss,  we  select  here  the 
former  as  being  the  more  likely,  and  proceed  to  adjust  the  discrepancies 
by  a  slight  increase  of  armature-length,  pole-diameter,  and  slot-area. 

It  is  to  be  noted  that  in  rough  preliminary  calculations  of  machines 
as  large  as  this  the  approximate  iron  loss  formula  of  p.  29  may  still 
be  used  as  it  was  throughout  in  the  case  of  the  smaller  machines.  For 
subsequent  more  accurate  approximations,  we  shall  make  use  of  the 
formula  on  p.  30,  in  which  the  iron  loss  in  the  teeth  can  be  separated 
from  that  in  the  armature  body. 


EXAMPLES   OF  PROCEDURE  IN   DESIGN         203 


TABLE  XXVII. 


Second  approximation. 
Six-poles.         200  K.W.         400  r.p.m.         500  volts. 


(8)  D  .         .        .        .        .        . 

32" 

(1)  d  .        .         .        .         ,        . 

9" 

(2)  Area  pole-core 

63  sq.  ins. 

(3)  Flux  per  pole         .      -  . 

63  x  105 

(4)  Flux  issuing  from  shoe  . 

55  X  105 

(5)  Area  of  shoe  face  .         .         . 

110  sq.  ins. 

(6)  Axial  shoe  length  . 

9" 

(7)  Pole-arc 

12-3" 

Ratio  pole-arc  to  pole-pitch   . 

0-73 

(9)  $ 

1-69 

(10)  Armature  conductors     . 

474  (nearest  even 

number) 

(11)  Ampere  wires  per  inch  . 

950 

(12)  D2L       

9220 

(13)  Depth  of  slot 

1-6" 

(14)  Net  copper  area     . 

30-4  sq.  ins. 

(15)  Area  per  conductor 

0-064 

(16)  Length  of  mean  turn 

64-5" 

(17)  Armature  resistance  (hot) 

0-0465  ohm 

(18)  Armature  resistance  loss 

7450  watts 

(19)  Voltage  drop  due  to  resist- 

ance ..... 

18-5 

(20)  Section   of    armature    below 

teeth 

37  sq.  ins. 

(21)  Radial  armature  depth  below 

teeth          .... 

5" 

(22)  Internal  diameter  of  stamping 

18-8" 

(23)  Weight  of  armature  core  ex- 

cluding teeth  and  slots 

760  Ibs.  (2700  cub.  ins.) 

Weight  of  teeth    . 

150    „    (530  cub. 

ins.) 

(24)  Frequency      .         .         . 

20 

Hysteresis  loss   in   armature 

body  

1010  (coefficient  = 

:  0-003) 

Eddy  loss  in  armature  body  . 

340 

Hysteresis  loss  in  teeth 

550 

Eddy  loss  in  teeth 

20 

Calculated  iron  loss 

1920 

The  latter  is  in  this  instance  a  good  deal  below  that  given  by  the  approxi- 
mate formula.     In  the  author's  opinion  1920  is  too  low,  and  2800  too  high. 


204     CONTINUOUS   CURRENT   MACHINE   DESIGN 

The  whole  subject  deserves  much  closer  consideration  than  it  has  hitherto 
received.* 

As  a  margin,  then,  for  possible  error,  we  shall  allow  an  increase  of 
10  per  cent,  over  the  last  calculated  value,  and  estimate  the  final  iron 
loss  at  2200  watts.  Thus — 

(25)  Estimated  iron  loss 2200 

(26)  Turns  per  armature  section       .         .         .1 

(27)  Number  of  Teeth. — This,  as  well  as  the  actual  slot  dimensions 
(No.  13),  depends  upon  conditions  rather  different  from  those  referred  to 
on  p.  190.  For  in  a  machine  of  this  size  round  wires  would  seldom  be 
used,  and  consequently  the  sectional  shape  of  the  armature  conductor  can 
be  made  to  suit  the  best  shape  of  slot  instead  of  vice  versa.  We  know 
that  the  number  of  conductors  will  be  about  474,  that  the  number  of 
slots  will  be  even  and  of  the  order  of  4D  (  =  128),  that  the  fewer 
the  slots  the  better,  and  that  the  number  of  conductors  must  suit  the 
formula — 

W  =  py  ±  2 

Now,  if  y  =  79,  W  =  476  or  472,  which  is  the  nearest  approach 
to  474.  We  then  obtain — 

,X7.  0,  ,  .,,  Conductors 

y  W  Slots  possible.  per  glot 

7q  /472     .         .     118  or  59     .         .     4  or  8 

\476     .  119          ..          4 

If  we  select  59  slots,  there  will  only  be  about  7  teeth  under  each 
pole-arc,  and  the  ampere- wires  per  slot  would  be  about  1600.  Such  an 
arrangement  (unless  the  slots  were  half  closed)  would  lead  to  great  field 
oscillation  as  each  tooth  passed  under  the  pole;  also  eddy-currents, 
humming,  and  possibility  of  sparking  would  result.  We  thus  decide 
upon  118  or  119  slots.  The  actual  choice  would  of  course,  in  practice, 
depend  upon  the  division  plates  available  on  the  stamping  machines.  We 
decide  on  118  slots. 

(28)  Commutator  sections        ...     236 

„  diameter      .         .  .  20" 

„  peripheral  speed  .  .  2100  f.p.m. 

(29)  ,,  friction  loss          .  .  570  watts 

(30)  „  C'R    .         .  .  800      „ 

*  Very  serious  discrepancies  are  sometimes  found  between  computation  and  test, 
which  have  never  been  properly  examined.  Thus  the  approximate  formula  given  on 
p.  29  shows  that  the  eddy  loss  is  almost  negligible  compared  with  the  hysteresis  loss, 
which  is  also  borne  out  by  the  values  just  calculated.  On  the  other  hand,  some 
writers  declare  the  eddy  loss  to  be  far  greater  than  that  due  to  hysteresis.  Thus  the 
author's  formula  on  p.  30  for  eddy  currents  gives  results  almost  four  times  those  of 
S.  P.  Thompson's  formula  (Dynamo  Electric  Machinery,  vol.  i.,  1904  ed.,  p.  104). 
And  the  values  given  by  Hawkins  and  Wallis  (The  Dynamo,  1908  ed.,  p.  633)  are 
for  eddy  currents  far  greater  than  even  the  author's  formula  would  yield. 


EXAMPLES   OF   PROCEDURE  IN   DESIGN          205 

Choice  of  Slot  Dimensions.  —  The  formula  upon  which  the  pro- 

visional slot  -depth  has  been  based  is  dependent  upon  the  ratio  -T—  —  73-7-1 

slot-  width 

as  shown  on  p.  15.  If  this  be  varied,  a  different  depth  and  area  of 
slot  results  even  when  the  tooth  density  is  maintained  constant.  In 
non-interpole  machines  a  great  depth  of  slot  leads  to  excessive  self- 
induction  with  consequent  sparking.  In  interpole  designs,  however,  this 
limit  does  not  exist.  If  for  ml  on'  p.  15  we  substitute  different  ratios  we 
shall  get  different  slot  depths,  and  now  that  the  number  of  teeth  is 
decided  the  corresponding  width  will  be  known,  so  that  we  can  tabulate 
as  follows  :  — 

Slot-pitch  =  0-85"  at  armature  circumference 

m,=  1  slot-depth  =  -05D  =1-6"  slob-width  =425"  slot  area  =  -68  sq.  in. 
,,=•8  „  =  -078D  =  2-5"  „  =-378"  „  =  -94  „ 

,,=•6        „          =-112D  =  3-6"  „         =-32"          „       =M5    „ 

It  is  then  seen  that  taking  a  value  of  ml  less  than  unity  leads  to  a 
larger  slot  area  ;  and  since  the  space-factor  is  constant  and  the  shape  of 
conductor  is  (within  limits)  adjustable,  this  is  a  very  clear  advantage. 
On  the  other  hand,  too  great  a  slot  depth  may  lead  to  so  much  flux- 
leakage  across  the  slot,  particularly  if  the  tooth-density  be  high,  that  the 
flux  embraced  by  the  lower  conductors  will  be  sensibly  less  than  that 
embraced  by  those  at  the  top  of  the  slot,  causing  a  diminution  of  E.M.F. 
and  the  possibility  of  eddy-currents  in  the  armature-bars. 

Maximum  Slot-area.  —  From  the  formula  on  p.  15  it  is  easy  to  find 
the  maximum  possible  slot-  area  now  that  D  and  the  densities  and  the 
tooth-pitch  are  known.  For  since  K  =  O405,  we  have  — 


Width  of  slot  =  ^ 
1  -\-ml 

The  product  of  these  two  is  the  area  of  the  slot,  which  may  be  written  — 


(1  -f  ™02  ^ 

The  differential  coefficient  of  this  expression  with  respect  to  ml  is  — 

8-05  -  1 


(1  +  m,)3 

Since  the  differential  coefficient  of  the  latter  with  respect  to  ml  is  nega- 
tive, when  equated  to  zero  it  will  give  the  value  of  ml  corresponding  to 
the  maximum  area  of  slot.  We  thus  obtain  — 

m,  =  0-42,  slot-depth   =  (H5D  =  4'8",  slot-width  =  0'25",   slot-area  =  1-2" 

So  that  up  to  a  ratio     .*!  ,    =  19-2,    the   area   of   the   slot    constantly 

increases. 

Now,  such  a  depth  as  4'8"  has  never  been  tried.     For  besides  the 


206     CONTINUOUS   CURRENT   MACHINE   DESIGN 

disadvantages  mentioned  on  the  previous  page,  the  bore  of  the  armature 
would  be  so  much  reduced  as  to  interfere  seriously  with  the  ventilation. 
Certainly  with  interpole  machines  designers  should  move  in  the  direction 
of  deeper  slots,  but  such  progress  must  be  made  with  extreme  caution. 
Thus  in  the  present  instance  the  author  would  consider  any  value  of  ml 
less  than  0'9  as  of  an  experimental  nature.  The  size  of  slot  we  decide 
upon  is  then  If"  x  y^",  which  corresponds  to  a  value  of  m^  =  0*98  about. 
There  is  no  object  in  this  case  in  rounding  the  bottom  corners  of  the 
slot  much,  because  with  rectangular  bars  very  little  is  gained  in  space 
factor  thereby. 

Slot  Insulation. — The  lining  of  the  slot  may  be  composite  and 
arranged  as  generally  indicated  in  Table  X.,  p.  146. 

We  thus  have  a  thickness  on  either  side  of  the  slot  of  say  50  mils. 
If  the  bars  are  covered  with  a  combination  of  double  cotton  and  braiding, 
a  thickness  of  O015"  on  either  side  must  be  allowed.  Since  there  are 
four  bars  per  slot,  they  may  be  arranged  as  in  the  sketch,  Fig.  89,  2,  p.  145, 
from  which  it  is  clear  that  the  maximum  thickness  of  copper  per  bar  will 
be  0-138".  It  is  always  necessary  to  allow  something  for  lack  of  uni- 
formity in  the  bars,  so  that  taking  0-014"  for  this  we  obtain  0'12"  as  the 
maximum  thickness  of  each  bar.  In  height  for  the  wooden  wedge  and 
clearance  0'22  inch  will  be  ample.  Beneath  this  a  strip  of  micanite  0'015" 
thick  may  be  placed,  while  between  the  upper  and  lower  bars  a  composite 
strip  0'03"  may  be  inserted.  This  leaves,  when  irregularities  in  the  bars 
are  allowed  for,  a  depth  of  about  0*6"  per  bar. 

A  net  area  of  copper  per  bar  of  0*072  sq.  in.  is  the  result  of  these  adjust- 
ments, comparing  very  favourably  with  the  value  0'064"  in  Table  XXVII 

Space  Factor. — The  space  factor  becomes  as  nearly  as  possible  0'4 
instead  of  the  value  0'38  allowed.  This  increase  is  largely  due  to  the 
use  of  a  two-circuit  winding,  which  requires  only  4  bars  per  slot.  With 
the  much  larger  number  required  by  a  multiple-circuit  winding  the  space 
factor  would  have  been  less  than  0'38. 

Losses. — The  corrected  values  are  as  follows  : — 

Variable. — Armature  copper-loss  .  .  .  6550 
Commutator  „  .  .  .  800 

Interpole 600 

7950 

Constant. — Armature  iron  loss  ....  2200 
Bearing  friction  ....  1200 
Commutator  friction  .  .  .  570 

3970 


Total  losses  excluding  shunt-winding  11,920 

Constant  losses  allowed  .         .          .     5250 
Shunt  loss  allowable        .         .         .1280 
Armature  Heating. — Total  power  to  be  dissipated  as  heat     8750 

From  Table  XXVI.  it  is  evident  that  by  any  method  the  temperature 


EXAMPLES   OF   PROCEDURE   IN   DESIGN          207 

rise  will  be  on  the  safe  side,  and  if  the  efficiency  is  to  be  a  maximum 
at  |  full  load,  one  may  increase  the  output  by  an  amount  corresponding 
to  a  variable  loss  of  1 300  watts.  This  is  an  increase  of  nearly  8  per  cent. , 
i.e.  the  output  becomes  215  K.W. 

Field-dimensions. — The  pole-area  and  diameter  being  settled,  and 
also  the  section  of  the  yoke  and  the  dimensions  of  the  pole-shoe,  there 
remains  the  length  of  the  field-pole.  This  is  determined,  as  in  previous 
examples,  by  approximating  to  the  field  ampere-turns  and  deducing  the 
area  required  from  temperature  rise. 

Gap  Ampere-turns. — 

Pole- pitch     .         .         .  .  .  .  16-7" 

Pole-arc         .         ....  .  .  12'3" 

Distance  between  pole-tips  .  .  .  4-4" 

Length  of  air-gap  .         .  .,  ,  .  0-125" 

Constant  (Table  III.  p.  40)  .  ..  .  3 -9 

Effective  pole-arc  .         .  .  .  .  12-79 

Effective  pole-arc  area   .  .  .  .  115  sq.  in. 

Density  in  gap  (no  slots)  .  .  .  48,000 

Tooth-width   /  !  N  l-Q3 

\  I)H^  f 


slot-width 
Slot- width 


3-5 


gap-length 

Constant  from  Fig.  26,  p.  41  .         .         .  1-27 

Actual  air-gap  density    ....       61,000 

Gap  ampere-turns  .......         2400 

Teeth  Ampere-turns. — 

Teeth  per  effective  pole-arc     .         .         .  15-2 
Tooth-width  at  top          .         .         .         .  0-4125 

Tooth-width  at  root        .         .         .         .  0-3275 

Mean  density 136,000 

Ampere-turns  (see  Fig.  27)    .         „  .         .         2600 

Ampere-turns  for  gap  and  teeth         .         .         .         .         5000 

Armature-core  Ampere-turns.— 

Density  in  core      .  .  .  .  75,000 

Length  of  mean  line       .         .  .  .  12" 

Ampere-turns  (Fig.  6)    .        ..  .  .,  * ••....         120 

If  as  a  first  approximation  we  allow  20%  of  the  above  total  for  the  yoke 
and  pole,  we  must  provide  altogether  for,  say,  6200  ampere-turns  per  pole. 

Allowing  10%  for  the  P.D.  across  the  shunt  rheostat  gives  -f-  or 
75  volts  across  each  field  coil ;  this  corresponds  to  a  shunt  current  of 
i2M}  or,  approximately,  2-56  amps.  Shunt  turns  per  pole  =  ^j-  =  2420. 
Thus,  if  the  calculated  ampere-turns  be  correct  the  loss  in  the  field  coils 
will  be  1140  watts  approximately,  and  in  the  rheostat  150  watts.  Thus 
watts  per  field  coil  =  190. 

Field-coil  Dimensions. — The  number  of  ampere-turns  being  small 
(because  of  the  interpoles),  it  will  probably  be  possible  to  avoid  using  a 


208     CONTINUOUS   CURRENT   MACHINE   DESIGN 

ventilated  coil.     We  try,  therefore,  first,  Case  II.,  p.  75,  and  assuming 
the  coil  to  be  wound  on  a  metal  former  without  taping,  we  adopt  — 

Ch  =  140  (p.  72),  T  =  60° 


Since  d  =  9",  ra  =  5",  allowing  for  the  spool,  and  the  two  equations 
for  the  coil  are  —  47/^4^^) 

450  =  47^+^i  +  6-28ZA+^<     .         .     (1) 

4  82  .  6200  .  6200  .  TT  .  (10  +  Qm2 
cc~v'  108xl90 

If  m2  be  taken  provisionally  at  1-6,  (2)  becomes  — 
lcdc  =  1-1(10  +  de) 

The  values  lc  =  7",  dc  -  If"  satisfy  theee  equations  nearly  enough. 

We  thus  obtain  a  pole  length  of  8",  and  the  field-winding  consists  of 
2500  turns  per  pole  of  a  wire  about  0-054"  diameter.  This  is  between 
Nos.  18  and  17  S.W.G.,  though  so  near  the  latter  that  probably  No.  17 
would  be  adopted  with  rather  more  shunt  resistance. 

Yoke  Dimensions.  —  Allowing  1"  for  the  thickness  of  the  pole  shoe 
in  the  centre,  and  adding  the  length  of  pole  and  air-gap,  we  get  as  the 
minimum  internal  diameter  of  the  yoke  50^".  It  will  be  necessary,  how- 
ever, as  the  field  coils  are  circular,  to  leave  a  flat  facing,  on  the  inside  of 
the  yoke  above  the  pole,  and  the  proper  thickness  of  this  is  best  obtained 
by  setting  the  machine  out  on  a  drawing-board.  We  shall  not,  however, 
be  far  wrong  in  taking  the  actual  internal  diameter  of  the  circular  part 
of  the  yoke  at  4'  4".  The  yoke  density  being  80,000  gives  the  yoke 
section  as  about  40  sq.  in.  Taking  a  width  of  14"  gives  us  a  mean  thick- 
ness of  about  2|".  The  main  over-all  dimensions  are  now  complete  with 
the  exception  of  the  interpoles,  so  that  the  total  ampere-turns  and  the 
value  of  the  leakage  factor  can  be  checked. 

Interpole  Dimensions.  —  We  shall  assume  in  this  example  that  the 
patents  mentioned  on  p.  151  are  not  to  be  used,  and  that  therefore  the 
axial  length  of  the  interpole  shoe  must  be  the  same  as  that  of  the  main 
shoe,  i.e.  9".  We  have  — 

Thickness  per  commutator  section    .         .  0*265" 

Brush  width    .  .  0-5" 

Sections  short  circuited    . 

Time  of  commutation       .         .  .  0*00127  sec. 

Turns  per  segment  ...         .1 

/"(seep.  122)  .....  460 

Lc  .......  0-0000092 

r  °  ......  0-0007 

-c  .     0-097 

Lc 

C"X*'  (Fig.  80)      '  ,       .„        .        .        .    0-93 


EXAMPLES   OF   PROCEDURE  IN   DESIGN        209 

e  (p.  121) 3-86,  say  3'9  volts 

Interpole  arc    ...  .     J" 

Time  coil  is  under  pole,  allowing  fringing  |  0-0015  sec 

factor  =  1'15  I 

Corresponding  flux  necessary     .  .     292,000  lines 

Interpole  shoe  area  with  fringe          .          .     9  sq.  ins. 
Approximateaverageair-gapdensity  allow-j  j    ? 

ing  for  increase  due  to  teeth  (p.  41)        ) 
Ampere-turns  for  gap       ,         •         •         •     1600 
Interpole   Ampere-turns. — The  width  of  the  interpole  arc   and 
the  flux  required  are  here  obtained  in  exactly  the  same  way  as  for  the 
smaller   machine.     On   account,   however,  of   the  greater  axial   length 
of  interpole-shoe,  the  leakage  factor  for  the  interpole  will  be  very  high. 
The  ampere-turns  per  pole  on  the  armature  to  be  neutralized  are  nearly 
7900,  so  that  the  total  interpole  ampere-turns  cannot  be  much  less  than 
9000.     These  act  in  conjunction  on  one  side  with  the  ampere-turns  of 
the  main  pole,  which  are  estimated  to  be  about  6200,  so  that  at  least 
15,000  ampere-turns  are  acting  across  the  gap  between  the  two  shoes. 
Now — 

Interpole-arc  =  |" 

Distance  between  main  pole-shoes  =  4 '3" 
Distance  between  interpole  and  main  shoe  =1*7  nearly 
Density  across  1-7"  due  to  15,000  ampere-turns  =  30,000 
If  we  assume  that  the  area  across  which  this  leakage  takes  place  is 
9"  long  by  |"  wide,  we  get — 

Total  leakage  flux  =  200,000  lines  at  least 
Now— 

Commutating  flux  =  292,000 

So   that   the   leakage  due  to  the  shoe  alone  corresponds   to   a   leakage 
factor  of  at  least  1'66,  and  therefore  we  must  assume  the  factor  for  the 
whole  of  the  leakage  flux  to  be  not  less  than  2. 
Thus— 

Flux  in  the  interpole  =  600,000 
Interpole  density  =  90,000 

Interpole  area  =  6'7  sq.  ins. 
Interpole  diameter  =  2*92  ins.,  say  3  ins. 

Now,  on  account  of  the  rather  small  space  between  the  poles  at  the 
inner  end,  and  assuming  that  the  interpoles  are  to  be  forgings,  it  is  more 
convenient  not  to  adopt  the  circular  section.  Instead  we  may  take  a 
section  2"  thick  and  3|"  long,  with  the  ends  of  the  section  rounded  so  that 
they  are  almost  semicircular.  The  ampere-turns  for  the  interpole  are 
then  as  follows  : — 

Reversing  armature  ampere-turns     .       -.         .     7866 

Ampere-turns  for  gap-flux          .         .         .         .     1600 

„  „         iron-circuit    .         .         .         .       160 

9626 
Turns  per  interpole  ^  =  24J 


CONTINUOUS  CURRENT  MACHINE  DESIGN 

To  obtain  this  number  of  ampere-turns  with  a  loss  of  100  watts  per 
coil  entails  a  resistance  per  coil  of  yg—  of  an  ohm.  It  will  be  necessary, 
therefore,  to  adopt  a  strip  of  about  0'37  sq.  in.  section,  and  this  winding 
will,  even  with  the  interpole  core  shaped  as  above,  barely  clear  the  main 
field  coil  windings  at  the  inner  end.  It  may  be  necessary,  therefore, 
either  to  wind  the  interpole  coil  taper  so  that  it  is  deeper  at  the  yoke 
end  where  there  is  plenty  of  room,  or  to  alter  the  shape  of  the  main  poles 
slightly  so  as  to  give  rather  more  clearance. 

Both  methods  are  in  use,  and  many  examples  of  either  are  to  be  seen 
among  modern  machines.  These,  however,  are  all  details  which  would  not 
be  definitely  decided  upon  until  the  final  design  for  the  output  was 
chosen.  It  is  sufficient  to  see  that  the  coils  can  be  made  to  clear  (as  is 
the  case  in  this  instance),  when  the  table  of  approximate  costs  can  be 
proceeded  with  as  on  p.  188  and  p.  196. 

Approximate  Cost  of  Net  Effective  Material. — Using  the 
prices  given  on  p.  175  as  a  guide  and  working  out  the  various  parts  of  this 
preliminary  design  we  get  the  following  list  of  costs  : — 

Iron — 

£     s.     d. 
Yoke     .         .        .         .         .     20     0     0 

Poles 900 

Shoes  .  .  .  .  .200 
Interpoles  .  .  .  .600 
Armature  core  .  .  .1900 

• £56     0     0 

Copper — 

Armature      .         .         .  14     0     0 

Shunt-field     .  .     22     0     0 

Interpole  copper  .  .  .  8  15  0 
Commutator  .  .  .  20  0  0 

£64  15     0 


Total  cost  of  effective  material       .         .         .     £120  15     0 

Assuming  the  ratio  of  total  works  cost  to  a  cost  of  effective  material 
as  2-5,  the  total  works  cost  of  this  machine  would  be  £300.  The  present 
market  price  (1910)  is  about  £340. 

Final  Design. — Having  completed  a  preliminary  design  as  above, 
other  sets  of  figures  on  similar  lines  can  be  worked  out  starting  with 
slightly  different  ratios.  From  these  the  most  economical  machine  can 
be  selected,  and  the  final  details  of  the  field  completed  very  much  as  has 
already  been  done  for  the  small  machine  in  Example  I. 


SERIES-WOUND  MACHINES. 

Generators  for  constant  E.M.F.  are  shunt  or  compound  wound.     Series 
winding  is  used  for  (1)  generators,  where  variable  E.M.F.  and  constant 


EXAMPLES   OF   PROCEDURE  IN    DESIGN        211 


current  are  required ;  (2)  motors,  where  variable  speed  and  torque  are 
required. 

Instances  occur  where  a  variable  E.M.F.  is  required  with  a  constant 
current.  This  is  so  in  the  case  of  arc  lamps  in  series  for  street-lighting. 
To  meet  these  demands,  machines  have  been  invented  which  will  auto- 
matically adjust  themselves  to  the  correct  P.D.  at  constant  current. 

Principle  on  which  Constant-current  Machines  work. — 
The  characteristic  of  a  series-wound  generator  running  at  constant  speed 
is  as  shown  (Fig.  125).  The  machine  of  course  only  excites  when  the 
circuit  is  closed. 

A  shunt  generator  gives  a  more  constant  E.M.F.,  as  shown  in  Fig. 


Current. 

FIG.  125.— SERIES  CHARACTERISTIC. 


Armature  Current. 
FIG.  126. — SHUNT  CHARACTERISTIC. 


126,  the  only  part  of  the  curve  used  in  practice  being  from  A  to  B. 
Beyond  B  the  voltage  is  very  unstable. 

Below  is  shown  a  circuit  with  arc  lamps  connected  in  series.  With 
such  a  connection  a  lamp  must  be  short-circuited  to  be  cut  out.  The 
current  then  tends  to  rise.  But  for  arc  lamps  an  almost  constant  current 
is  required,  so  that  the  P.D.  must  be  decreased  to  check  this  rise.  For 


FIG.  127.— SERIES-WOUND  GENERATOR 
WITH  ARC  LAMPS  IN  SERIES. 


Current.  Ct  C2 

FIG.  128.— CONSTANT-CURRENT 
CHARACTERISTIC. 


these  conditions,  then,  the  part  BO  of  the  curve  in  Fig.  125  would  be 
suitable,  since  the  P.D.  decreases  as  the  current  rises.  With  a  view  to 
using  this  part  of  the  curve,  machines  have  been  designed  to  give  a  rapid 
fall  from  B  to  C,  this  drop  occurring  at  the  current  required.  Then  for 
a  small  change  in  current  from  ct  to  c2,  Fig.  128,  we  get  quite  a  large 


212     CONTINUOUS   CURRENT   MACHINE   DESIGN 

change  in  P.D.  If  by  short-circuiting  a  lamp  the  current  tends  to  rise, 
a  very  small  increase  of  current  quickly  brings  down  the  P.D.  to  the 
value  required.  This  machine  is  thus  to  a  certain  extent  self-regulating, 
the  change  in  current  only  being  small,  and  full  armature  current  is 
obtained  on  complete  short  circuit  only,  i.e.  at  "no"  P.D. 

Design  of  Constant-current  Machines. — We  require  a  machine 
which  shall  possess  as  steep  a  characteristic  as  possible  between  B  and  C, 
Fig.  128.  Keeping  in  mind  the  ordinary  series  generator,  we  remember 
that  this  fall  BC  is  due  to— 

(1)  Saturation,  which  brings  the  curve  horizontal,  and 

(2)  Armature-reaction,  which  in  destroying  the  main  field  brings  the 

curve  down. 
Hence,  in  designing,  it  is  necessary — 

(1)  To  have  at  the  maximum  P.D.  all  the  iron  parts  saturated. 

(2)  To  arrange  the  machine  so  that  from  B  to  0  the  armature-reaction 

is   heavy,    i.e.    so   that   on  short   circuit  the  current   is  little 

different  from  that  at  maximum  P.D. 

Now,  armature-reaction  is  proportional  to  armature  AT  for  a  given 
field,  but  there  is  a  limit  to  the  armature-reaction  possible  with  good 
commutation.  We  may  thus  say  that — 

(1)  The  number  of  commutator  segments  must  be  as  large  as  will 

keep  the  reactance-voltage  (Vr)  down  to  about  two  volts  per 
segment. 

(2)  With  the  current  at  which  the  machine  is  supposed  to  run,  the 

armature-reaction  should  be  sufficient  to  distort  the  field  very 
considerably,  i.e.  the  ratio — 

Armature  AT    .  .   1-5  or  2 

field  AT      should  aPProach  -— 

The  effect  of  armature-reaction  is  more  marked  if  the  brushes  are 
given  a  greater  lead,  i.e.  if  the  back  AT  are  increased.  This  makes  the 
curve  much  steeper,  but  at  the  same  time  decreases  the  maximum  P.D. 
obtainable,  as  the  brushes  are  not  in  the  position  of  maximum  E.M.F. 

Movement  of  Brushes. — The  machine  can  be  made  self-regulating 
if  the  curve  is  steep  to  start  with,  and  if  as  the  number  of  lamps  decreases 
the  brushes  are  automatically  moved  forward.  This  is  the  principle  of 
the  patent  of  the  "Thomson-Houston  arc-lighting  generator." 

The  above  is  an  outline  of  the  design  of  constant-current  series 
generators.  The  subject  is  too  special  and  limited  to  require  further 
treatment  here,  but  attention  may  be  directed  to  the  paper  on  the 
subject  by  Prof.  Wilson  before  the  I.E.E. 

Series  Motors. — For  a  motor  the  only  part  of  the  characteristic 
used  is  from  A  to  B  (Fig.  124).  An  increase  in  load  means  an  increase 
in  the  field,  and  as  torque  is  proportional  to  the  product  of  field  and  of 
armature  AT,  the  torque  varies  as  the  square  of  the  current  up  to  the 
point  of  saturation,  and  then  approximately  as  the  current.  Now,  for  a 
shunt  motor  the  torque  varies  almost  as  the  armature  current.  Hence 
a  series  motor  is  used  where  for  a  given  armature  current  a  large  torque 
is  required,  and  where  a  large  range  of  speed  is  desired. 


EXAMPLES   OF   PROCEDURE   IN    DESIGN         213 

Series  motors  are  used  for  two  purposes — 

(1)  Traction. 

(2)  Lift  and  crane  work. 

For  lift  work,  however,  to  prevent  excessive  speed,  a  compound  motor 
is  often  preferred.  The  tendency  is  thus  to  design  series  motors  for 
traction,  and  to  fit  them  in  for  crane  work  if  desired. 

Traction  Motors. — For  traction  work  the  following  points  have  to 
be  remembered : — 

(1)  The  available  space  is  very  small. 

(2)  It  is  important  to  keep  the  weight  of  the  machine  down,  as  it 

has  to  be  moved  about  with  the  car. 

(3)  The  motor  must  be  designed  so  that  it  will  stand  exceptionally 

heavy  strains. 

In  railway  work  the  motor  armature  is  placed  directly  on  the  wheel  axle. 
For  tramways  three  systems  have  been  used — 

(1)  Armature  directly  coupled  to  axle. 

(2)  Armature  with  single  gearing. 

(3)  Armature  with  double  gearing. 

Type  (2)  is  practically  the  only  one  now  adopted.  Type  (3)  was 
found  to  be  noisy,  inefficient,  and  difficult  to  maintain,  whereas  (1)  required 
a  large  size  of  motor,  and  vibration  was  transmitted  to  the  machine 
from  the  road. 

The  size  of  motor  used  for  average  tramcars  is  from  20  to  30  H.P., 
and  for  single  gearing  the  ratio  is  about  5  to  1,  the  number  of  teeth  in 
the  pinion  being  about  14,  and  in  the  wheel  67  to  68. 

The  pinion  is  machine  cut,  and  made  of  hard  steel. 

The  wheel  is  also  machine  cut,  but  of  soft  steel. 

Width  of  pinion,  4"  to  5". 

Efficiency,  about  80  per  cent,  with  the  gearing  (see  Fig.  19),  and 
maximum  efficiency  is  at  \  to  j  full  load. 

The  weight  of  a  25  H.P.  motor  is  about  1500  Ibs.  complete  with  the 
case. 

Problem  III. 
27-H.P.  Series  Motor. 

Limiting  Dimensions. — The  dimensions  are  settled  to  some 
extent  by  the  size  of  the  car.  A  25  to  30  H.P.  motor  will  have  to  run  at 
such  a  speed  that  when  driving  a  car  wheel  of  30"  diameter,  the  speed  at 
full  load  will  be  about  10  miles  per  hour. 

Taking  the  gear  ratio  4 -8,  this  gives  a  motor  speed  at  full  load  of 
550  to  600  r.p.m.  The  speed  is  thus  fixed.  The  maximum  current  is 
decided  by  the  voltage  of  the  system,  and  taking  this  at  500  volts,  full 
load  current  =  50  amps. 

The  general  proportions,  densities,  etc.,  are  not  different  from  those 
adopted  in  ordinary  practice  as  discussed  in  Chapters  II.  and  III. ;  but 
there  are  certain  conditions,  notably  those  of  small  weight  and  short 
rating,  which  to  some  extent  modify  the  ordinary  values.  The  following 
are  some  usual  figures  : — 


214    CONTINUOUS   CURRENT   MACHINE   DESIGN 

Density  at  the  pole-face  .     50,000  to  70,000  lines  per  sq.  in. 

Density  in  the  yoke     f  .     90,000  lines  per  sq.  in. 

Leakage  factor  about  .  .     1  *25 

Number  of  poles  .         .  .4 

Type  of  Winding. — As  all  the  surface  of  the  commutator  cannot 
be  seen,  the  winding  will  conveniently  be  two-circuit  with  two  brushes 
at  90°,  preferably  arranged  at  the  top  of  the  commutator. 

Poles. — These  are  invariably  laminated,  and  sometimes  space  blocks 
are  used  to  form  ventilating  ducts  parallel  with  and  opposite  to  those  in 
the  armature. 

Temperature  Rise. — Traction  motors  are  always  totally  enclosed, 
and  usually  rated  at  their  full  load  for  one  hour  with  a  rise  of  temperature 
not  exceeding  55°  C.  on  any  part.  Since  the  efficiency  is  about  80%  (see 
Fig.  19),  of  which  about  5%  is  lost  in  the  gear,  we  shall  have  the  following 
preliminary  values  of  losses  for  a  27  H.P.  motor  : — 

Output         .         .         .  20,000  watts  on  second  motion  shaft. 

Input  ....  25,000  watts  or  50  amps,  at  500  volts. 

Loss  in  gear  5%    .         .  1250  watts. 

Other  losses          .         .  3750  watts. 

The  latter  must  be  dissipated  as  heat  by  the  motor. 

The  input  is  about  42  watts  per  revolution  per  minute,  which  from 
curves  like  those  of  Fig.  49,  when  the  higher  temperature  has  been  allowed 
for,  corresponds. to  about  1  sq.  in.  of  external  surface  for  each  watt  dissipated. 
About  3700  sq.  ins.  of  external  surface  are  thus  seen  to  be  necessary. 
From  trial  designs,  or  by  reckoning  out  the  external  surface  corresponding 
to  such  motors  as  are  illustrated  in  Example  I.,  it  is  soon  seen  that  this 
value  corresponds,  in  the  case  of  a  four-pole  machine,  to  an  armature 
diameter  of  from  12"  to  14".  Accordingly  we  find  in  practice  that  traction 
motor  armatures  are  usually  about  this  diameter.  It  would  be  convenient 
in  many  cases  to  make  the  armature  larger  in  diameter  than  the  above, 
but  the  standard  30"  wheel  leaves  then  but  little  clearance  between  the 
bottom  of  the  motor  and  the  road,  unless  the  centre  line  of  the  motor  is 
brought  very  much  above  the  wheel  axle,  when  the  yoke  tends  to  foul  the 
car  floor. 

Commutation  Limits. — It  has  already  been  shown  in  connection 
with  Problem  I.  that  a  reasonable  value  of  Vr  without  interpoles  corre- 
sponds to  a  maximum  of  five  turns  per  section.  Again,  in  Problem  IV. 
an  instance  is  given  of  the  connection  between  flux  per  pole  and  turns 
per  section  for  constant  Vr.  Applying  the  latter  to  this  case,  or  arguing 
from  the  former,  leads  to  the  conclusion  that  4  turns  per  section  would  be 
a  large  number  to  adopt,  and  three  turns  per  section  would  lead  to  a 
value  of  Vr  quite  high  enough.  In  spite  of  this,  up  to  the  present  four 
turns  per  section  have  been  mostly  used,  though  commutation  is,  in  the 
author's  opinion,  unsatisfactory  with  this  number.  Three  turns  per 
section  leads  to  a  machine  rather  more  costly,  but  unless  interpoles  be 


EXAMPLES   OF   PROCEDURE  IN   DESIGN        215 

universally  adopted  this  type  of  armature  will  certainly  be  more  generally 
used,  as  the  commutator  lasts  much  longer. 

Division  of  Losses. — The  various  losses  cannot  be  treated  quite 
in  the  same  way  as  for  constant-speed  machines,  because  all  the  losses  are 


now  more  or  less  variable.  The  iron  loss  varies  both  with  the  speed  and 
current,  and  since  the  speed  rises  when  the  current  falls,  probably  the 
iron  loss  remains  more  or  less  constant.  The  sum  of  the  friction  and  iron 
losses  rises  as  the  speed  falls,  but  not  very  rapidly.  Thus  in  the  case  of 
such  a  motor  tested  at  the  Municipal  School  of  Technology,  Manchester, 


216    CONTINUOUS    CURRENT   MACHINE   DESIGN 

the  sum  of  the  iron  and  friction  losses  only  varied  from  780  watts  to  900 
watts,  while  the  speed  changed  from  500  to  200  r.p.m. 

Table  XXVIII.  and  Figs.  129, 130,  and  131  give  particulars  of  a  crane 
or  traction  motor  for  500  volts,  designed  on  the  principles  outlined  above, 
with  three  turns  per  commutator  section.  The  student  will  find  it  a  good 
exercise  to  start  from  first  principles,  as  was  done  in  the  case  of  Problems 
I.  and  IT.,  and  work  towards  the  dimensions  given. 


TABLE  XXVIII. 


Type  of  Machine         . 

H.P 

Revolutions  per  minute 

Poles          .         .         .         .         .      .  . 

Armature — 

Armature  diameter    . 

Core-length 

Pole-pitch 

Pole-arc 

Pole-face  area 

Flux  issuing  from  shoe 
Generated  volts  at  full  load 
Number  of  slots         .... 
Coils  per  slot      . 
Turns  per  coil    . 
Length  of  mean  turn  . 
Armature  conductors 
Size  of  conductor       . 

Slot-depth 

Slot-width 

Slot  arrangement       . 

Armature  resistance  .         .         .         . 

Tooth-root  density      . 

Radial  depth  of  stamping  below  teeth 

Stamping  arrangement 

Density  below  teeth  .... 

Diameter  of  shaft  in  centre 

Diameter  at  gearing  journal 

Over-all  length  of  armature 

Armature  arrangement 


Series  Motor 

27 

600 

4 

13-5" 

8" 

10-6" 

7-5" 

60  sq.  ins. 

3  X  106 

450 

41 

3 

3 

40" 

738 

No.  13  S.W.G. 

1JL" 

0* 

as  Fig.  130 

0-4  ohm  hot  (70°  C.)  nearly 

164,000  (uncorrected) 

Fig.  102 
100,000 

2|" 

16" 
Fig.  129 


Binding  Wires. — On  the  core  there  will  be  three  bands  of  binding 
wire  (tinned  steel),  each  band  consisting  of  about  12  turns  of  No.  18 
S.W.G.  On  the  end-connections  at  each  end  there  will  be  one  band  con- 
sisting of  about  18  turns  of  No.  16  S.W.G. 

Armature  Core-heads  or  End-plates. — These  are  partly  shown 
in  Fig.  129.  They  are  made  in  malleable  iron. 


EXAMPLES   OF  PROCEDURE  IN   DESIGN        217 


Commutator  (see  Fig.  129)— 

No.  of  segments    .... 
Thickness  of  segment  (max.) 
Insulation  thickness 
Current  density  under  brush 
Brushes  per  spindle       .      ,  .  -    ?. 
Axial  length  of  brush   . 
Thickness  of  brush 
Coils  short  circuited  at  each  brush 


123 

0-25" 

0-03" 

40  amps,  per  sq.  in. 

2 

2" 

i" 

3 


EMPIRE  CLOTH 
TAPES 

T*f»E 

CONDUCTOR  OVER 
TAPE 

TAPES  &  VARNISH 
FILLING,-  IN  Piece 
&  VARNISH 


CONDUCTOR  OVER  INIU^TION 
TAPE 

TAPES   &  VARNISH 
CLOTH 


H875  TOTAL 


FIG.  130. — ARMATURE  SLOT  DETAILS. 


Where   the   commutator   bush  fits  the  shaft,  the   latter   should   be 


218     CONTINUOUS   CURRENT   MACHINE   DESIGN 

slightly  tapered  and  the  bush  fixed  on  by  a  key.  The  bush  is  generally 
solid  cast  iron  (no  spider). 

The  depth  of  segment  allowed  for  wear  varies,  being  often  stated  in 
the  specification ;  it  generally  lies  between  -*-"  and  1"  (1"  is  excessive); 
take  |".  This  gives  1"  from  top  of  segment  to  the  top  of  the  bush.  The 
thickness  of  the  end  rings  (which  are  of  mica)  is  rarely  less  than  /-",  and 
the  ends  of  these  rings  are  bound  down  with  string. 

Field-magnet. — The  length  of  the  air-gap  varies  with  different 
makers,  being  often  specified  when  the  motors  are  ordered.  As  a  maxi- 
mum y  is  used,  but  for  A.C.  motors  it  may  be  as  small  as  J".  In  the 
present  design  we  take  fg". 

Density  in  pole     .         .         .     100,000 

Flux  per  pole        .         .         .     3  X  106  x  1'25  =  3-75  x  106 

Section  of  pole-core      .         .     37'5  sq.  ins. 

If  the  axial  length  of  the  pole-core  be  the  same  as  that  of  the  arma- 
ture, and  if  these  cores  have  space  blocks  to  allow  of  an  air  circulation  in 
the  pole  itself,  and  to  reduce  eddy-currents  therein,  then  the  net  axial 
length  of  the  pole  is  the  same  as  that  of  the  armature,  viz.  6-3".  The 
width  of  the  pole  is  then  6".  This,  however,  is  in  the  author's  opinion 
unnecessary.  It  is  desirable  that  some  space  blocks  be  used,*  and  if  two 
y  each  are  adopted  in  place  of  two  of  J"  each,  the  net  axial  length  of  the 
pole  is  6-8"  and  its  width  5-5". 

Yoke  Dimensions. — It  is  not,  as  a  rule,  advisable  to  consider  the 
length  of  yoke  carrying  flux  as  much  greater  than  the  armature  gross 
length,  say  in  this  case  10".  Thus  fixing  upon  a  density  of,  say,  90,000 
for  the  yoke  (it  being  of  good  steel),  we  get  the  necessary  area  as  20'7 
sq.  in.,  and  the  thickness  as  2". 

Losses. — The  armature  iron-loss  at  full  load  when  estimated  by  the 
rough  formula  (p.  29)  is  720  watts. 

Bearing  friction  estimated  at  1%     .  .     220  watts 

Commutator  resistance  loss  (cf.  Fig.  83)     130      ,, 
Commutator  friction  loss         .         .                42      ,, 

Armature  resistance  loss         .         .  .  1000      ,, 

The  sum  of  the  above  losses  is  2112,  which  subtracted  from  3750  leaves 
roughly  1600  watts  for  the  series  field  and  various  losses  not  calculated, 
such  as  eddy-currents  in  the  pole-shoes,  etc.  If  we  calculate  the  field  for 
1500  watts,  the  losses  should  be  on  the  safe  side. 

Field  Ampere-turns. — The  following  table  gives  the  calculated 
values  of  field  ampere-turns  at  full  load  : — 

*  Otherwise  with  such  wide  armature  ducts  flux  tends  to  pass  down  the  teeth 
flanks  at  each  duct,  setting  up  thereby  considerable  eddy-currents  even  in  the 
space-blocks  of  the  armature. 


EXAMPLES   OF  PROCEDURE   IN   DESIGN        219 


Part. 

Material. 

Density. 

Length. 

Amp. 
turns 
per  inch. 

Amp. 
turns. 

Armature  core 

wrought  iron  (special) 

100,000 

3-4" 

30 

102 

Teeth     .     .     ... 

»                » 

(154,000) 
1  (mean)  I 

1-1875 

2,600 

3000 

Gap  .     .     .     . 

air 

54,000 

0-1875 

17,000 

3180 

Pole  .... 

wrought  iron 

100,000 

3J 

30 

94 

Yoke     .     .     . 

cast  iron 

90,000 

10 

30 

300 

Total  .    6676 

To  the  above  must  be  added  an  allowance  for  armature- reaction. 
Since  the  motor  has  to  be  reversible,  the  brushes  must  short-circuit  coils 
lying  midway  between  the  pole-tips,  i.e.  there  will  be  no  back  ampere- 
turns.  The  distorting  (or  cross)  armature  ampere-turns  with  a  current 
of  50  amps,  will  be  2300.  The  constant  from  Fig.  39  is  0-34.  Therefore 


FIG.  131.— TRACTION  MOTOR  FIELD-COIL.    SKETCH  OF  DETAILS. 

the  compensating  ampere-turns  are  780,  so  that  the  total  ampere-turns  to 
be  provided  per  pole  are  in  round  numbers  7500. 

Field  Coil. — With  a  current  of  50  amps.  150  turns  per  coil  will  be 
needed,  and  for  1500  watts  lost  the  resistance  per  coil  must  be  0-15  ohm. 
Fig.  131  shows  the  least  room  that  will  be  taken  up  by  a  coil  consisting 
of  150  turns  of  wire  of  square  section  of  0*18"  side,  having  a  resistance  of 
0-144  ohm.  In  this  diagram  A  and  B  show  the  completed  coil,  and  C 
is  the  half -spool  used  to  support  and  fix  the  coil.  For  traction  purposes, 
where  space  is  of  great  importance,  such  a  coil  would  be  of  advantage,  but 
for  lift  or  crane  work  it  would  be  prefer  able  to  adopt  a  coil  consisting  of 


220     CONTINUOUS   CURRENT   MACHINE   DESIGN 

150  turns  of  say  No.  5  S.W.G.  with  a  larger,  longer  pole.  The  space-factor 
in  the  latter  case  would  be  worse  and  the  machine  larger.  But  these  dis- 
advantages would  usually  be  more  than  compensated  for  by  the  greater 
ease  of  winding.  Square  and  rectangular  wires  are  very  difficult  to  keep 
flat  and  always  tend  to  cut  the  insulation. 

Problem  IV. 

The  preceding  problems  have  all  dealt  with  the  derivation  of  new 
machines.  Often,  however,  the  designer  is  faced  with  the  question  of 
making  the  best  of  an  old  design  to  suit  new  conditions.  Very  often  it 
is  a  matter  of  altering  a  machine  designed  for  a  voltage  such  as  230,  so 
that  it  may  be  suitable  for  400  or  500  volts.  Such  a  case  is  the  following  : — 

A  standard  four-pole  220-volt  machine,  having  an  armature-core  12|" 
diameter  X  8"  long  with  75  slots  and  75  commutator  bars,  is  required  to  be  re- 
modelled so  astobe  suitable  for  16  K.W.  500  volts,  and  400  r.p.m.,  ivith  a  re- 
actance-voltage (Vr)  not  exceeding  three.  The  original  flux  was  2|  million 
lines  per  pole,  which  should  not  be  exceeded,  or  alteration  of  yoke  and  pole 
will  be  necessary.  Give  the  minimum  number  of  commutator  segments  that 
will  be  required  for  satisfactory  operation  without  substantial  alteration  to  the 
flux. 

Now,  we  know,  to  begin  with,  that  the  original  number  of  slots  is  in- 
conveniently large,  and  that  some  number  in  the  neighbourhood  of  39 
would  be  more  economical.  This  only  means  that  there  must  be  a  change 
in  the  number  of  coils  per  slot ;  it  gives  no  clue  to  the  number  of  turns 
per  coil.  To  ascertain  the  limits  of  the  latter,  we  first  substitute  in  that 
formula  for  Yr  which  is  in  terms  of  the  watts,  poles,  and  flux  per  pole,  and 
is  given  on  p.  128. 

In  this  formula  the  values  are  as  follows  : — 

EC  =  16,000  watts 
Net  armature  length  —  6" 
Pole-pitch  =  10" 

Vr  =  3  volts 

consequently  we  obtain  the  relationship — 

Flux  =  4  x  105  x  (t.p.s.) 

Taking  now  the  E.M.F.  formula,  and  assuming  that  the  maximum 
voltage  to  be  generated  at  the  normal  speed  of  400  r.p.m.  is  460  volts,  we 
have — 

E  =  flux  x  conductors  x  n  X  2  x  10~8  for  a  two-circuit  winding 
Substituting  for  the  values  of  voltage  and  speed,  we  get — 
Flux  X  conductors  =  345  x  107 

But  flux  =  4  x  10s  X  (t.p.s.),  from  the  preceding  formula,  and  con- 
ductors =  (t.p.s.)  X  2s,  where  s  is  the  number  of  sections,  so  that — 

s(b.p.s.)2  =  4312 


EXAMPLES   OF   PROCEDURE  IN   DESIGN        221 
We  now  tabulate  as  follows  :  — 

Sections.  Turns  per  section.  Flux  per  pole. 

141  5-5  2*2    x  106 

123  5-9  2-36  x  106 

111.  .         .         6-2         .  2-8     x  106 

It  is  then  clear  that  without  increasing  the  original  flux,  the 
maximum  possible  number  of  turns  per  section  at  this  speed  is  6,  and  that 
this  number  corresponds  to  123  sections. 

Thus  the  machine  reaches  its  limit,  as  far  as  reactance-voltage  is  con- 
cerned, when  arranged  with  41  slots,  3  coils  per  slot  (i.e.  6  half-coils), 
6  turns  per  coil. 

Problem  V. 

Of  a  similar  character  to  the  last  problem  is  the  question  that  arises 
when  it  is  necessary  to  determine  the  best  radial  depth  of  iron  below  the 
teeth.  This  is  of  importance  up  to  the  point  of  saturation,  because, 
though  the  total  ampere-turns  are  hardly  affected,  yet  the  less  the  radial 
depth  the  better  is  the  internal  ventilation  ;  and  it  is  therefore  important 
to  know  how  the  iron  losses,  which  increase  with  the  density,  will  be 
affected  by  the  change  in  radial  depth.  To  make  the  question  more 
clear,  consider  the  following  general  case  :  — 

A  four-pole  machine  having  an  armature  D"  diameter  at  the  tooth  roots, 
witli  gross  length  I"  and  net  length  //',  has  to  carry  N  lines  per  pole.  What 
will  be  the  best  radial  depth  of  stamping  from  the  point  of  view  of  tempera- 
ture-rise and  efficiency,  assuming  the  iron-loss  formula  of  p.  29  as  correct? 

Let  D;  be  the  internal  diameter  of  the  stampings,  then  — 

Vol.  of  iron  in  armature  below  the  teeth  =  j  (  D^  —  Dt.2  k 
Sectional  area  of  iron  in  the  armature  =  —  l—^  —  *  ^ 

Corresponding  density  =  ^r  -  =p-r 

"~ 


The  frequency  is  constant,  so  that  — 

Iron-loss,  neglecting  teeth  =  (Di  -f  Dz)  X  constant 

i.e.  the  smaller  D^  the  better  is  the  efficiency. 

Now,  from  Fig.  46  the  cooling  surface  is  proportional  to  — 


where  nd  is  the  number  of  ducts,  and  LA  is  the  length  of  the  armature 
including  end  connections. 

Differentiating  this  with  respect  to  Dt,  we  get  — 


222     CONTINUOUS   CURRENT   MACHINE   DESIGN 

and  the  cooling  is  therefore  a  maximum  when  — 

+  2)  =  I 


Thus  the  answer  to  the  question  is  that  the  armature  losses  increase 
with  an  increase  of  the  hole  Da  but  so  also  does  the  cooling  surface  up  to 
the  point  when 

Ufa  +  2)  =  21 

The  best  density  will  therefore  depend  upon  the  particular  machine. 
The  fact  that  the  teeth  have  been  neglected  does  not  affect  the  argument, 
provided  that  the  slot  depth  is  a  constant  fraction  of  D,  as  it  will  be  by 
the  formula  of  p.  15.  The  best  density  in  any  particular  case  can  easily 
be  deduced  from  the  above  formulae;  it  will  evidently  depend  on  the 
frequency,  iron-loss  constant,  number  of  ventilating  ducts,  and  the  con- 
stant chosen  in  the  temperature-rise  formula  (method  2),  and  it  is  always 
subject  to  the  limitations  of  saturation,  and  the  proportion  of  D;  occupied 
by  the  shaft. 

As  a  particular  instance,  let  D  =  13*5",  Dx  =  11",  Lj  =  17",  I  =  8", 
1L  =  6-3",  ~  =  20,  nd  =  2,  N  =  3  x  106.  Iron  loss  constant  =  1-8.  These 
data  correspond  almost  with  Fig.  129. 

Then  iron  losses  due  to  iron  below  teeth  =  261  +  24Df. 

Cooling  surface  is  a  maximum  when  D^  =  4*3". 

This  results  in  a  density  of  about  68,000  lines  below  the  teeth. 
When  the  shaft,  however,  is  considered,  this  would  leave  too  little 
passage  for  air,  so  that  practice  modifies  the  results  to  some  extent,  as  is 
seen  by  reference  to  Fig.  102. 


APPENDIX   I. 

RELATIONSHIP  BETWEEN  DEPTH  OP   SLOT,  DIAMETER  OF  ARMATURE,  AND 
MAGNETIC   DENSITIES. 

Let  ws  =  width  of  slot  ; 

wt  =  width  of  tooth  at  the  armature  periphery  ; 
t  =  number  of  teeth. 

Then  at  the  armature  periphery  — 

ws  -f  wt  +  7rD/t. 

Let  ws  =  ml  .  wt,  so  that  w^  is  a  ratio  and 

wt  =  7rD/(l  +  mjt  ;  ws  =  7rDm1/(l  +  mjt. 

Let  D6  =  the  diameter  of  the  armature  measured  at  the  bottom  of 
the  slots,  then  — 

Width  of  tooth-root  =  -n-Db/t  -  7rDm1/(l  +  mjt 
7riD6(l  +  ,»1).-mi)Dj 
t  \  1  +  ml  } 

Let  /?j  =  average  density,  at  the  roots  of  the  teeth  ; 
/  =  net  iron  length  of  the  armature  core. 

Then— 


Flux  per  tooth  .  .     .     (1) 

Now  let  rp  =  ratio  of  pole-arc  to  pole-pitch  ;  then  — 

Pole-face  area  =  L  .  ?rD  .  rp/p 
Let  B/  be  the  average  density  at  the  pole-face  ;  then  — 

Flux  issuing  from  the  pole-face  =  j3JJ~LTrDrp/p    .     .     (2) 

Now,  the  number  of  teeth  carrying  the  flux  is  t  .  rpm2/p,  where  m.2  is  a 
ratio  greater  than  unity  to  allow  for  the  "  fringing  "  which  takes  place  at 
the  pole  -tips. 

Multiplying  (1)  by  the  number  of  teeth  gives  us  the  total  flux  carried 
by  the  teeth  per  pole  ;  its  value  is 


224  APPENDIX  II 

Evidently  this  flux  must  be  the  same  as  that  given  by  (2). 
Thus— 

D6(l  +  mi)  -  mj) 


fttlm2  1  +  wij 

Putting  §f  —  =  K,  and  transposing  — 
pefcwi2 

KD(1  4-  1%)  =  D6(l  +  OTJ)  -  mxD 
D  1  4-  ml 


or  ^-  = 


D6      K(l  +  «h)  4-  TOI 


In  order  that  this  may  be  positive, 

1  must  be  >  K(l  +  w^) 

orK.  <r-^  — 
1  +»»! 

As  an  example,  if  ^,/ft  =  1/2-7,  //L  =  0-8,  %  =  1-1,  wij  =  1  ;  then 

K  =  0-42  and 
depth  of  slot  =  0-04D 


APPENDIX   II. 

THE  CONNECTION  BETWEEN  THE  EFFICIENCY  OP  THE  MACHINE    AND   THE 
RESISTANCES  OF  THE  CIRCUIT. 

IN    any   electric    generator    the   electrical   efficiency    is   given    by    the 
expression  — 

watts  output 

Electrical  efficiency  =  —  77  -  -  —  T—  ;  —  \  —  T~-  —  n  - 
J       watts  output  4-  electrical  losses 

In  the  case  of  a  series-wound  machine  this  is  — 
Electrical  efficiency  =  EC/{EC  4-  C2(Rrt  4-  B,)}  =  E/{E  4-  C(Ra  4-  B/ 


From  which  it  is  clear  that  the  electrical  efficiency  is  a  maximum  when 
(Ra  -}*  R/)  is  a  minimum. 

In  the  case  of  a  shunt-wound  generator,  however,  there  is  a  particular 
relationship  between  the  various  resistances  in  the  circuit  for  which  the 
electrical  efficiency  is  a  maximum. 

Let  V}!  be  the  electrical  efficiency  of  the  machine  ;  then  — 

watts  output         __  EG  _ 
=  watts  output  +  losses  -  E0  +  (c  +  J^  +  (|R/ 


APPENDIX   II.  225 

Now,  let  R  be  the  external  resistance  corresponding  to  the  current  C. 

Then  C  =  E/R,  and 
W  .    (W      /E   ,    EV        ,  /E 

+ 


1    _L  «  4-     JL  -L          4.          l' 

"  R/  ^  R  "^R,      R/ 

Now,  when  ^  is  a  maximum  it  is  clear  that  the  denominator  (M)  in  the 
foregoing  expression  must  be  a  minimum.  Differentiating  M  with  respect 
to  R  and  equating  to  zero,  we  have  — 

**-_?*+».+l-0  (2) 

dR~       R'  +  R/^R,"- 

daM  _  2R_a 
dW  ~~  W  ' 
which  is  positive,  so  that  (2)  will  be  a  minimum. 

/  R,R;  /~1*7~      a\ 

From  (2)  we  get  R  =  V  R^fR,  =  R/  V  B7+  B,  ' 
[Usually  Rrt  is  small  compared  with  R/}  so  that  ^  is  a  maximum  when— 

R  = 


or  R  =  V^a 

In  order  to  tind  the  value  of  r/t  when  it  is  a  maximum,  we  substitute 
(3)  in  the  denominator  M,  thus  — 


M  (minimum)  =  1  +  2  ^  + 


whence  ^(max)  =  1  -4-  {l  +  2  1^  +  2  ^  ^/l  +  5 

This  leads  to  the  quadratic  equation  — 


with  the  solution  Ra  =  R,^    7  ^^ 

4^, 

And  substituting  the  value  of  Ra  in  the  equation 

R  -  T{  ^  /      K« 

K  -  K^  V  RTR: 


gives  B,  =  R 
and  R,,  =  R 


226 


APPENDIX   III. 


These  values  correspond  to  the  maximum  point  of  the  electrical  efficiency 
curve. 

In  compound-wound  machines  two  cases  arise.  For  the  long-shunt  type 
the  above  relationships  are  true  if  Rrt  be  held  to  include  the  resistance 
of  the  series  coils.  For  the  short-shunt  type  a  slight  but  practically 
negligible  change  is  introduced  owing  to  the  compound  loss  being  pro- 

(          E  \  2 
portional  to  C2  instead  of  (  C  +  TV    )  . 

The  electrical  efficiency  ^  is  not  always  easy  to  assume  or  derive ;  but 
the  application  of  these  relationships  to  rj,  the  commercial  efficiency,  is 
given  on  p.  27. 

APPENDIX  III. 
CALCULATION  OP  LEAKAGE  FLUX. 

On  pp.  42  and  43  the  main  considerations  governing  the  calculation 
of  leakage  flux  have  been  mentioned.  The  amount  of  flux  leaking  from 
one  surface  to  another  being  difficult  to  estimate,  it  is  useful  to  have  at 
hand  a  few  standard  cases  founded  on  broad  assumptions  which  yield 
useful  approximate  values.  The  six  cases  given  below  (the  first  three 
of  which  are  due  to  Professor  Forbes)  are  examples  of  such  useful 
standards.  In  each  case  it  is  assumed,  for  the  reasons  given  on  p.  43, 
that  the  reluctance  of  the  iron  part  of  the  leakage  path  may  be  neglected. 
The  distribution  of  flux  forming  the  basis  of  the  calculations  is,  of  course, 
far  from  being  exactly  in  accordance  with  that  which  actually  exists, 
but  it  yields  values  for  the  flux  which  are  found  to  be  sufficiently  accurate 
for  practical  purposes. 

Case  I. — Leakage  between  two  parallel  surfaces  (Fig.  132)  of  areas 
A!  and  Ao  respectively.  The  lines  of  induction  are  assumed  to  be 
straight,  as  indicated  in  the  figure. 

Flux  =  ampere-turns  x  « •  j—*- 


FIG.  132.— LEAKAGE  FLUX.  CASE  I.  FIG.  133. — LEAKAGE  FLUX.    CASE  II. 

Case  II. — Leakage  between  two  parallel  surfaces  in  approximately  the 


APPENDIX   III. 


227 


same  plane,  separated  by  a  short  gap  (Fig.  133).     The  lines  of  induction 
are  assumed  to  be  semicircles  as  indicated. 

r., 

1     . 

—  dr 

ampere-turns 
- 


Case  HI.  —  Leakage  between  two  parallel  surfaces  in  approximately  the 
same  plane  separated  by  a  comparatively  long  gap  (Fig.  134).  The  lines  of 
induction  are  assumed  to  be  straight,  with  quadrants  at  the  ends  as  indicated. 


FIG.  134. — LEAKAGE  FLUX.    CASE  III. 


Flux 


__  ampere-turns 
0-313 

__  ampere-turns 
0-313 


/         TTT  -f-  d 
logl°  ~~ 


NOTE. — Obviously,  if  the  surfaces  are  not  parallel,  but  are  inclined  to 
one  another  at  an  angle  0,  the  circular  measure  of  this  angle  is  to  be 
substituted  for  TT  in  both  Case  II.  and  Case  III. 

Case   IV. — Leakage   between  parallel  surfaces  (or  slots'),  with  electric 


il. 


h — w— H 

FIG.  135. — LEAKAGE  FLUX.    CASE  IV. 


conductors  passing  between. — In  Fig.  135  let  the  slot  shown  be  supposed  full 


228 


APPENDIX   III. 


of  conductors,  /  in  number,   each  carrying  a  amperes.     Then   the  flux 
across   any  section   Jdx  is    due  to  -•,--  ampere-conductors,    and    may   be 

written     Flux  through  dx  = 


Total  flux  across  the  slot  = 


xdx 


/  1    depth  of  slot 

=  0^313  x  ampere-conductors  x  5  •  widthofslot 

If  the  slot  is  not  completely  filled,  but  a  space  is  left  empty,  this  space 
can  be  treated  under  Case  I.  Leakage  from  teeth  to  neighbouring  iron 
can  be  taken  by  Carter's  curve  (see  p.  47). 

Case  V. — Leakage  between  surfaces  projecting  from  a  yoke  and  inclined 
to  one  another  at  an  angle  0,  with  electric  conductors  carrying  current  evenly 
distributed  down  them. — This  case  is  that  which  occurs  in  the  field 
magnets  of  a  multipolar  machine,  and  is  illustrated  in  Fig.  136.  The 


B 


FIG.  136. — LEAKAGE  FLUX.    CASE  V. 


flux  may  be  assumed  as  passing  frpm  surface  to  surface,  following 
concentric  circular  paths  between  the  planes  AB  and  CD,  or  it  may  be 
supposed  to  pass  straight  across  in  parallel  lines  from  one  side  to  the 
other.  The  latter  supposition  yields  results  more  nearly  approaching 
those  taken  from  practical  measurement. 

Let  t.a.  be  the  total  ampere-conductors  lying  between  the  pair  of 
surfaces,  and  let  W  be  the  distance  AB,  and  h  be  the  projected  length  AC. 
Then— 

t.a.l                   x 
The  flux  along  a  strip  dx  •—  ,.0101.  X  ^dx 


Total  flux  = 


APPENDIX   III. 
t.a.l 


229 


Thus  for  a  4-pole  machine  tan  ^  =  1 ,  and  the  leakage  flux  is — 
t.a.l    /     h      2-3W  W      \ 

Case  VI. — Flank  leakage.  In  a  machine  with  poles  of  rectangular 
section,  to  the  leakage  between  pole  and  pole  as  in  Fig.  136,  must  be 
added  that  which  takes  place  between  the  flanks  or  side-faces  of  the 


FIG.  137. — LEAKAGE  FLUX.    CASE  VI. 


poles  as  suggested  in  Fig.  137.  This  leakage  may  be  estimated  by  a 
method  combining  Case  III.  with  Case  V.  If  we  assume  that  each 
projection  in  Fig.  137  is  wound  from  end  to  end,  so  that  acting  across 
the  space  between  each  pair  there  is  the  magneto- motive  force  due  to 
the  ampere-turns  on  the  pair,  and  if  the  lines  of  induction  be  supposed 
straight  in  the  middle  with  quadrants  at  the  ends  as  indicated  in  the 
figure,  then — 
Leakage  flux  from  one  flank  to  the  next 

•x  =  h    f*r  =  r 

ampere-turns  x 


/•x  —  ft    /»r  =  r 
J  x  =  oJ  r  =  0 


0-313& 


W  -  2rx  +  TTT 


drdx 


23o  APPENDIX   IV. 

ampere-turns r 2-3  W  -  2rh  -f  irr       I   J2-3W2         W  - 

~  0-313A7T      L~2"  ^ l0^10      W  -  2rk      +  4?  1  ~2~  logl°  ~~^W 


2-3(W  +  irQ2!         W  -  2rft  +  ?rr\       Tir^T 
2~          lo&o     W  +  7rr        f""IrJ 

f\ 
in  which  T  =  tan^(=  1  for  a  four-pole  machine). 


APPENDIX   IV. 

RELATIONSHIP  BETWEEN  LENGTH  AND  DEPTH  OF  FIELD-COIL  (le  and  dc), 

FIG.  44. 

The  resistance  of  any  coil  is — 

(specific  resistance  of  copper)  X  turns  X  length  of  mean  turn 
area  of  wire 

The  fall  of  potential  across  the  coil  for  a  given  field  current  is — 
(spec,  res.)  X  amp. -turns  X  length  mean  turn 
(dia.  wire)2  X  ^ 

length  of  coil  x  depth  of  coil  * 

Now,  turns  per  coil  =  — -^ : — - — ~-r. — ^ — 

(dia.  wire  +  insulation)" 

We  may  write — 

diameter  of  wire  -f-  insulation  =  w(diameter  of  wire) 
where  m  is  a  multiplier  which  will  vary  with  each  wire.     Thus — 

ampere- turns  per  coil  _  lc  X  dc 

field  current  m8  X  (dia.  wire)'2 

Substituting  the  value  for  the  diameter  of  the  wire  as  obtained  from 
(2)  in  (1),  we  obtain — • 

,   __  4  spec.  res.  X  (amp.-turns  per  coil)2  X  length  mean  turn  X  «t2 

TT  watts  per  coil 

The  value  of  the  specific  resistance  should  be  that  corresponding  to 
the  mean  temperature  of  the  coil.     Say  82  x  10~8. 

*  There  is  no  allowance  for  bedding. 


APPENDIX   V.  231 


APPENDIX   V. 
THEORY  OP  PURE  E.M.F.  COMMUTATION. 

In  any  closed  circuit  the  sum  of  the  P.D.'s  is  zero.    Now,  in  the  short- 
circuited  coils  under  the  brush  there  are  three  P.D.'s  acting,  viz.  — 

(1)  The  P.D.  clue  to  the  current   passing  through  a  circuit   having 
resistance  :  if  C;  be  the  instantaneous  value  of  the  current  at  a  time  t 
seconds  after  the  commencement  of  commutation,  this  P.D.  is  C?:r,  where 
r  represents  the  resistance  in  the  circuit  at  the  time  t.     This  resistance 
is  made  up  of  the  resistance  of  the  brush,  the  brush  contacts  and  the 
coil.     Since  we  are  now  dealing  with  pure  E.M.F.  commutation,  we  shall 
allow  nothing  for  the  changing  area  of  brush  contact,  so  that  r  becomes 
constant  and  may  be  taken  to  be  the  resistance  of  the  coil  plus  the  least 
resistance  the  brush  ever  offers.     The  latter  may  be  very  small,  for  with 
proper  E.M.F.  commutation,  such  as  is  secured  with   interpoles,  there 
should  be  no  necessity  for  high-resistance  brushes. 

(2)  The  P.D.  due  to  self-induction,  i.e.  due  to  the  changing  magnetic 
flux  set  up  by  the  current  itself.     If  Lc  be  the  coefficient  of  self-induction 

of  the  coil,  this  P.D.  has  a  value  =  ^Lc—^~  . 

(3)  The  P.D.  set    up  in    the  coil    due    to  its  rotation   through    the 
magnetic  field  under  the  interpole,  or  pole-  tip.     This  we  will  call  e. 
Thus  we  have  — 


or 


Integrating  —  ~- 1  =  log,,  — log,,  A 

where  A  is  the  integration  constant. 

Now,  at  the  beginning  of  commutation,  i.e.  at  time  t  =  0 — 
C;  =  current  per  conductor  =  CM 


or 


Thus 


At  the  end  of  commutation,  when  t  •-  tet  Ct  should  have  a  value  =  —  Cw, 


232  APPENDIX   VI. 

ithout 

e  -  Cwr 


if  the  brush  is  to  leave  the  segment  without  spark.     Under  these  con- 
ditions — 


_  £ «       e  -  0. 

or  *    i, 


e  4-  C,,r 

i.e.  e  = 

1  _  e~L-c<< 

This  really  shows  the  value  of  e  necessary  at  the  end  of  commutation,  i.e. 
at  the  critical  moment  when  a  segment  leaves  the  brush.  It  is,  how- 
ever, sufficient  for  interpole  calculations  to  proportion  the  interpole  and 
its  windings  so  that  an  E.M.F.  at  least  equal  to  e  may  be  introduced. 


APPENDIX  VI. 

ARMATURE-DIMENSIONS  AND  REACTANCE-  VOLTAGE. 
From  p.  127  we  have  — 

2C,,Sn(m  +  eppxtpsy 

*  r   —  }Q8  .....        V.V 

Now,  I  =  0-8d  nearly  (p.  20). 

Consider  first  the  case  of  circular  poles.     We  have  from  p.  20  — 

d  =  l-oXD/p 
Suppose  the  average  value  of  X  to  be  1-15  ; 

then  D  =  pd/I-73 
Also  the  pole-pitch  (p.p.)  =  vD/p  —  Trrf/1'73 

so  that  40Z  +  6pp  =  32d  +  10'9d  =  43d   .     .     .     (2) 


w 
whence  V,  =  -    ^—    *  ......     (3) 

For  square  poles  the  corresponding  form  is  — 

93^(»2SK.CL  ^ 

r  ~  108  ......     ^  ' 

The  use  of  the  above  formulae  may  be  extended  by  introducing  the 
total  watts  with  which  the  machine  is  dealing.  It  is  necessary  to  dis- 
criminate between  two-circuit  and  multiple-circuit  windings,  because  of 
the  difference  in  the  value  of  CL  in  the  two  cases. 


APPENDIX   VI.  233 

A.  Multiple-circuit  Windings. 
In  this  case,  since  — 

E  =  flux  per  pole  X  armature  conductors  x  n  x  10~8 
and  since  conductors  =  2  x  armature-turns  =  2S  X  tps 

and  C  =  Cw  X  p 
we  have  EC  =  2  X  flux  per  pole  X  Bn(tps)Cwp  x  10~8 

Now,  from  equation  (1)  above  — 

2Sn(«pg)Ow10-8  =  Vr/(40Z  + 
whence 

_  flux  per  pole  x  p  X 


or  V}.  =  watts  ^  —  ,/v^  y,  —  ....     (5) 

flux  per  pole  x  poles 

Substituting  from  equation  (2)  above,  we  get  in  the  case  of  circular 
poles  — 


fl   -- 

flux  per  pole  x  poles 
and  for  square  poles  — 

^T  46-5d  .  (tps)  „.. 

V    =  watts  „  —          —  Y-^     —  1  —  approximately  .     .     (7) 
flux  per  pole  x  poles    FP  / 


If  we  assume  a  magnetic  density  in  the  pole  of  105  fearna  per  sq.  in., 
we  get  for  circular  poles  — 

Vr  =  0*55  kilowatt  per  pole  x  turns  per  section  -7-  pole-diameter    (8) 
and  for  square  poles  — 

Vr  =  0'465  kilowatt    per  pole  X  turns    per  section  —  length  of   pole 
side     .      ................     (9) 

B.   Two-circuit  Windings. 

In  the  case  of  multiple-circuit  windings  the  number  of  turns  lying 
between  two  neighbouring  commutator  segments  is  simply  the  number 
of  turns  per  section.  In  two-circuit  windings,  however,  the  number  of 
turns  between  two  neighbouring  segments"  is  p/2  times  the  number  of 
turns  per  section.  Also,  since  selective  commutation  is  liable  to  take 
place  in  two-circuit  windings  when  as  many  sets  of  brushes  are  used  as 
there  are  poles,  it  is  advisable  to  assume  the  use  of  only  two  sets  of 
brushes. 

Then  the  number  of  turns  short  circuited  per  segment  =  (tps)  X  jp/2  ; 
so  that  Vr  for  a  two-circuit  winding  is  under  these  conditions  p/2  times 
Vr  for  a  multiple  circuit  winding  having  the  same  number  of  turns  per 
section. 


234 


APPENDIX   VII. 


APPENDIX   VII. 
WIRE  TABLES. 


1 

Number  Diameter, 
S.W.G.   inches. 

j 

Area, 
sq.  inches. 

Weight, 
Ibs.  per 
1000  yds. 

Resistance  (ohms) 
per  1000  yards. 

Number 
S.W.G. 

Cold  =  15°  C. 

Hot=60°C. 

30 

0-0124 

0-000121 

1-4 

199-1 

233-4 

30 

29 

0-0136 

0-000145 

1-676 

165-5 

194-4 

29 

28 

0-0148 

0-000172 

1-989 

139-8 

163-8 

28 

27 

0-0164 

0-000211 

2-440 

113-8 

133-5 

27 

26 

0-018 

0-000254 

2-942 

94-48 

111 

26 

25 

0-020 

0-000314 

3-633 

76-53 

90 

25 

24 

0-022 

0-000380 

4-392 

63-24     74-4 

24 

23 

0-024 

0-000452 

5-233 

53-13 

62-1 

23 

22 

0-028 

0-000616 

7-120 

39-05 

45-9 

22 

21 

0-032 

0-000804 

9-301 

29-90 

35-1 

21 

20 

0-036 

0-001018 

11-77 

23-62 

27-7 

20 

19 

0-040 

0-001257 

14-53 

19-13 

22-4 

19 

18 

0-048 

0-001810 

20-93 

13-28 

15-6 

18 

17 

0-056 

0-002463 

28-48 

9-762 

11-5 

17 

16 

0-064 

0-003217 

37-20 

7-478 

8-8 

16 

15 

0-072 

0-004072 

47-09 

5-904 

6-95 

15 

14 

0-080 

0-005027 

58-13 

4-784 

5-6      14 

13 

0-092 

0-006648 

76-88 

3-617 

4-2      13 

12 

0-104 

0-008495 

98-24 

2-831 

3-33 

12 

11 

0-116 

0-01057 

122-2 

2-275 

2-66 

11 

10 

0-128 

0-01287   148-8 

1-868 

2-18 

10 

9 

0-144 

0-01629   188-4 

1-476 

1-73      9 

8 

0-160 

0-02011 

232-5 

1-195 

1-4       8 

7 

0-176 

0-02433 

281-3 

0-9881 

1-16      7 

6 

0-192 

0-2895 

334-7 

0-8307 

0-972     6 

5 

0-212 

0-03530 

408-20 

0-6813 

0-798 

5 

4 

0-232 

0-04227 

488-80 

0-5688 

0-666 

4 

3 

0-252 

0-04988 

576-70 

0-4821 

0-567  !    3 

2 

0-276 

0-05983 

692-00 

0-4019 

0-48      2 

1 

0-300 

0-07069 

817-60 

0-3402 

0-4      1 

1/0 

0-324 

0-08245 

953-40 

0-2917 

0-342 

1/0 

2/0 

0-348 

0-09511 

1099 

0-2528 

0-3 

2/0 

3/0 

0-372 

0-1087 

1257 

0-2212 

0-26 

3/0 

4/0 

0-400 

0-1257 

1453 

0-1913 

0-224 

4/0 

APPENDIX   VIII.  235 

APPENDIX  VIII. 
SPECIFIC  RESISTANCE  OF  COPPER  AT  VARIOUS  TEMPERATURES. 

Resistance  per  inch 
Temp,  degrees  C.  cube  in  ohms. 

0 63  X  10-8 

10 65  x  10~8 

15  .    .    .    .    .  67  X  10-8 

20 68  x  10~8 

30  ...  71  x  10-8 

40  .    .    .    .    .  73  x  10-8 

50  .    .    .    .    .  76  x  10 -8 

60  .    ....    .  78  x  10-8 

70  .    .    .    .    .  81  x  10-8 

80  84  x  10-8 


INDEX 


The  numbers  refer  to  pages 


Adamson's  crane  motors,  145 
Air-gap,  area  of,  39-42 
Air-gap,  density  in,  13,  39-41 
Air-gap,  length  of,  13, 14 
Ampere-turns  of  armature,  34,  55,  56 
Ampere -turns,  back,  53,  54 
Ampere-turns,  compounding,  57 
Ampere-turns,  constancy  of,  14 
Ampere-turns,  cross,  53,  54,  187 
Ampere-turns  for  interpole,  124,  195,  209 
Ampere-turns,  total,  56,  57,  187,  219 
Analysis  of  machines,  182,  199 
Appearance,  importance  of,  34 
Armature  coils,  fixing  of,  163,  164 
Armature  core  density,  16,  221 
Armature  core  heads,  159 
Armature  distance  pieces,  161 
Armature  end  connections,  11, 162 
Armature  end  plates,  159 
Armature  and  field  relationship,  20,  Chap. 

Armature,  general  form  of,  11 
Armature  laminae,  insulation  of,  147 
Armature,  length  of,  20,  33 
Armature  losses,  32,  33  — 
Armature,  peripheral  speed  of,  24 
Armature  reaction,  Chap.  V. 
Armature  reaction,  effect  on  main  field, 

52,  53 

Armature  reaction,  flux  due  to,  51 
Armature      reaction      in      neutralized 

machines,  61 

Armature  reaction,  limits  due  to,  60-62 
Armature  reaction,  vector  representation 

of,  51,  52 

Armature  slots,  depth  of,  15 
Armature  slots,  number  of,  15,  16,  185, 

204 

Armature  teeth,  density  in,  15 
Armature  windings,  Chap.  VIII. 
Armature  windings,  chord,  96 
Armature    windings,    circuits    through, 

100,  106 


Armature  windings,  closed  coil,  88 
Armature  windings,  commutator   pitch 

of,  92,  109 
Armature  windings,  comparison  of   lap 

and  wave,  115,  116 
Armature  windings,  creep  of,  108 
Armature    windings,   developments,   96, 

106 

Armature  windings,  drum,  11,  92  et  seq. 
Armature  windings,  drum  resistance  of, 

96,  107 
Armature    windings,    drum    and    ring 

windings  compared,  92,  93 
Armature  windings,  dummy  coils,  115 
Armature  windings,  duplex  lap,  97 
Armature  windings,  duplex  ring,  97 
Armature    windings,    equalizing    rings, 

104,  105 

Armature  windings,  idle  coils,  115 
Armature      windings,     lap      (see      also 

MULTIPLE  CIECUIT),  94  et  seq. 
Armature    windings,    multiple    circuit, 


Armature    windings,    multiple     circuit, 

rules  for,  103,  104 
Armature    windings,    multiple    circuit, 

multiplex,  98 

Armature  windings,  notation,  98,  101 
Armature  windings,  number  of  slots,  115 
Armature  windings,  open  coil,  88 
Armature  windings,  pitch  of,  91,  93,  99, 

109 

Armature  windings,  progressive,  93, 108 
Armature  windings,  re-entrancy,  89,  100, 

103,  109 

Armature  windings,  retrogressive,  94, 109 
Armature  windings,  ring,  90,  91 
Armature  windings,  ring,  resistance  of, 

90 

Armature  windings  in  slots,  111-114 
Armature  windings,  slot  pitch,  111,  112 
Armature  windings,  two  circuit,  105 
Armature  windings,   two    circuit,  rules 

for,  109 
Armature  windings,  types  of,  88 


INDEX 


237 


Armature  windings,  wave,  105,  109 
Arnold,  Prof.,  on  heating  of  armatures, 

81 
Arnold,  Prof.,  on  field  coils,  71 


BARBEL  winding,  11 

Bearings,  153-155 

Bearings,  ball,  154  (Fig.  124) 

Binding  wires,  216 

Brushes,  friction  losses,  133 

Brush-gear,  165-166 

Brush-gear,  insulation  of,  147 

Brush-holders,  166-169 

Brush-holders,  Verity's,  168 

Brush,  number  of  segments  per,  135 

Brushes  per  arm,  135 

Brushes,  pressure  drop  due  to,  131 

Brushes,  properties  of,  130,  131 

Brushes,  rockers,  166 

Burge  and  Macfarlane  on  ampere-turns, 

62 
Burge  and  Macfarlane  on  temperature 

rise,  82 


CAST  iron,  use  of,  3,  4 
Cast  steel,  use  of,  3,  4 
Coils.     See  FIELD  COILS,  etc. 
Commutating  poles,  121 
Commutating  poles,  flux  in,  123,  124 
Commutation,  Chap.  IX. 
Commutation,  calculation  of,  121 
Commutation,  E.M.F.,  120 
Commutation  coils,  120 
Commutation  in  drum  armatures,  119 
Commutation,  frequency  of,  118 
Commutation  limits,  135,  215 
Commutation,  methods  of,  119,  120 
Commutation,  resistance,  124-126 
Commutation  in  ring  armature,  117 
Commutation  by  special  pole-tips,  121 
Commutation,  theory  of,  231 
Commutators,  cost  of,  176 
Commutators,  design  of,  133, 135, 164, 165 
Commutators,  examples  of,  185,  217 
Commutators,  general  form  of,   11,  12, 

164,  165 

Commutators,  insulation  of,  147,  148 
Commutators,  length  of,  33, 133 
Commutators,  peripheral  speed  of,  24 
Commutators,  pitch  of,  92 
Commutators,  temperature  rise  of,  86 
Compounding  ampere-turns,  57-60 
Compound  coils,  construction  of,  58 
Compound  coils,  calculation  of,  59 
Compound  coils,  losses  in,  30,  31,  124 


j   Constant  current  generators,  211,  212 
I   Constant  losses,  25,  28-30 
i   Constant    pressure   machines,   examples 
of,  182,  197 

Constant    pressure    machines,   analysis 
of,  182,  199 

Costs,  Chap.  XI. 

Costs  of  commutators,  176 

Costs,  effect  of  design  ratios  on,  176-178 

Costs  of  effective  material,  174,  175 

Costs,  empirical  methods,  175 

Costs,  examples  of,  172,  173, 188, 196, 210 

Costs,  modern  tendency  in,  180 

Costs,  ratios,  174 

Costs,  subdivision  of,  170,  171 

Costs,  total  works,  171 

Costs  of  yoke,  178,  179 

Cotton  fabrics  as  insulators,  137 

Cramp,  W.,  on  magnetic  leakage,  69 

Crane  motors,  Adamson's,  145 

Crane  motors,  design  of,  88,  213 


D2L,  22,  23,  83-86,  183,  201 

Density  in  air  gap,  13,  39 

Density  in  armature  core,  16,  221 

Density  in  teeth,  15,  42 

Density  in  brushes,  129,  131 

Density,  examples  of,  182, 199 

Density  in  pole,  13 

Density  in  yoke,  13 

Dielectric  strength,  138,  139 

Dimensions  and  output,  21,  22,  60-62, 
85,  86,  132,  133,  183 

Drum  windings.  See  ARMATURE  WIND- 
INGS 

Dummy  coils,  115 


E 


EDDY  currents  in  poles,  7 

Eddy  current  losses,  29,  30,  204 

Effective  material,  cost  of,  174,  175 

Efficiency,  average,  26,  28 

Efficiency,  commercial,  27 

Efficiency  curve,  shape  of,  25 

Efficiency,  electrical,  25 

Efficiency  and  losses,  Chap.  III. 

Efficiency,  Maximum,  25-27,  Appen- 
dix II. 

Electric  loading  (X),  21,  62,  177,  184, 
200 

Enclosed  machines,  losses  in,  31 

Enclosed  motors,  temperature-rise  of, 
65,  87,  88 

End  connections,  11,  162 

End  plates,  159,  216 


238 


INDEX 


Equalizing  rings,  304,  105 
Establishment  charges,  171 
Examples  of  binding  wires,  164,  216 
Examples  of  brush  surface,  136,  186 
Examples,  constant  pressure  machines, 

182,  197 

Examples  of  densities,  182,  199 
Examples  of  division  of  losses,  30,  186, 

201,  202,  206,  215,  218 
Examples  of  field   coils,  141,  142,  208, 

219 

Examples  of  interpoles,  193-195,  208,  209 
Examples  of  maximum  slot  area,  205 
Examples    of    number    of    commutator 

sections,  185, 217 

Examples  of  number  of  poles,  201 
Examples  of  number  of  teeth,  185,  204 
Examples,  range  of  outputs,  192 
Examples  of  reduction  of  cost,  188 
Examples  of  relationship  of  D  and  L,  20, 

200 

Examples  of  series  motors,  210  et  seq. 
Examples  of  slot  arrangement,  144,  145, 

192,  206,  217 
Examples  of  slot  dimensions,  191,  192, 

205 
Examples    of    slot   insulation,   144-147, 

190,  206 

Examples  of  space  factor,  147,  183, 206 
Examples   of   temperature   rise,  77,  84, 

85,  186,  187,  202,  214 
Examples  of  voltage  and  current,  183 
Examples  of  yokes,  178,  208,  218 


F 


FABRICS,  cotton,  137 

Fibre,  vulcanized,  137 

Field  and  armature  relationship,  20, 
Chap.  V. 

Field-coil,  berrited  wire  for,  69 

Field-coil  calculations,  Chaps.  IV.,  V., 
VI. 

Field-coil,  examples  of,  141, 142,  208, 218, 
219 

Field-coil,  fixing  of,  149,  151 

Field-coil,  insulation  of,  141,  142 

Field-coil,  maximum  and  mean  tempera- 
ture of,  68 

Field-coil  space-factor,  140,  141 

Field-coil,  temperature  of,  Chap.  V. 

Field-coil,  ventilation  of,  74,  75,  77,  150 

Field-coil  losses,  31 

Field-coil  magnets,  machining  of,  152, 
153 

Formulae,  reliance  on,  181 

Frequency  of  commutation,  118 

Friction  losses,  27,  133 

Friction  losses  of  brushes,  133 


H 

I   Hawkins,  C.  C.,  on  leakage-factor,  43 
Heat,  causes  of,  63 
Heating-coefficients,  71,  73 
Heating-coefficients      of      coils.         See 

TEMPERATURE-RISE 
Heating  and  cooling,  laws  of,  64,  65 
Hiss  atid  Page  on  temperature-rise,  62 
Hobart,  H.  M.,  on  commutation,  122 
Hobart,  H.  M.,  on  temperature  rise,  71, 81 
Hysteresis  losses,  29,  30,  186,  204 


Idle  coils,  115 

Insulation,  Chap.  X. 

Insulation  allowances,  57,  58,  139 

Insulation  and  maximum  temperature, 

69 

Insulation  of  wires,  139 
Interpole  ampere-turns,  124 
Interpole,  examples  of,  194-196,  208,  209 
Interpole,  fixing  of,  151 
Interpole,  Phoenix  patent,  151 
Iron,  cast,  use  of,  3,  4 
Iron  losses,  18, 19,  185,  204 
Iron  losses,  estimation  of,  29,  30 
Iron,  malleable,  5 
Iron,  wrought,  3,  4,  17,  27 


LAHMEYER  magnet,  9 
Laminated  poles,  7,  149 
Laminae,  insulation  of,  147 
Lap-windings.   See  ARMATURE-WINDINGS 
Leakage-factor,  42-49,  and  Appendix  III. 
Leakage-factor,  examples  of,  45 
Leakage  between  poles,  Appendix  III. 
Leakage  between  shoes,  ibid. 
Leakage,  slot,  47 

Loading,  electric.     See  ELECTRIC  LOAD- 
ING 
Loading,     magnetic.       See     MAGNETIC 

LOADING 

Losses  in  armature,  32,  33 
Losses  in  compounding,  31,  124 
Losses,  constant,  35 
Losses,  division  of,  28-31 
Losses,  eddy,  29-30,  204 
Losses,  effect  on  enclosing,  31 
Losses  in  enclosed  machines,  31 
Losses,  example  of  division  of,  30,  186, 

201,  202,  206 
Losses  in  the  field,  31 
Losses  and  efficiency,  Chap.  III. 
Losses,  friction,  27,  133 
Losses,  hysteresis,  29,  30,  185,  204 
Losses,  iron,  estimation  of,  18,  19,  29,  30 


INDEX 


239 


Losses,  ratio,  constant  to  variable,  31 

Losses,  variable,  25 

Lundell  motors,  11 

Lustgarten,  J.,  on  temperature  rise,  71 


M 


Macfarlane  and  Burge.     See  BURGE 
Machines,  form  of,  Chap.  I. 
Machines,  general  proportions,  Chap.  II. 
Magnetic  circuit,  calculations  for,  Chap. 

IV. 

Magnetic  circuit,  corrections  to,  39,  49 
Magnetic  circuit,  general  form,  1,  2 
Magnetic  loading  (Y),  21-62;   177,  184, 

200 

Magnetization  curve,  49 
Manchester  dynamo,  9 
Mica  and  micanite,  139 
Multiple  circuit  windings.     Sec  ARMA- 

TDEE  WINDINGS 


N 


NATIONAL  Physical  Laboratory  on  tem- 
perature rise,  71 . 

Neu  Levine  and  Havill  on  temperature 
rise,  71 

Neutralization,  34,  54 

Neutral  position,  52 


O 


OUTPUT  and  dimensions,  21-22,  60-62, 

85-86,  132,  133-183 
Outputs,  range  of,  192 


Page  and  Hiss  on  temperature  rise,  62 

Paper  insulation,  137-138 

Peripheral  speed  of  armature,  24 

Peripheral  speed  of  commutator,  24 

Pitch,  91,  93 

Pitch,  commutator,  92 

Pitch  of  lap  windings,  99 

Pitch  of  slot  winding,  111,  112 

Pitch  of  wave  windings,  109 

Pole-arc,  effective,  40 

Pole-arc,  ratio  to  pole  pitch,  14 

Pole  pitch.     See  POLE-ABC 

Poles,  commutating.     See  COMMUTATING 

POLES 

Poles,  density  in,  13 
Poles,  diameter,  output  in  terms  of,  183 
Poles,  eddy  currents  in,  7 
Poles,  fixing,  5,  15,  149 
Poles,  hollow,  6 


Poles,  number  of,  11,  201 

Poles,  shape  of,  7,  8 

Pole-tips,  6 

Press-spahn,  137 

Pressure  and  current,  32,  33 

Progressive  winding,  93,  108 

Proportions,  general,  of  machines,  Chap. 


BATING  for  continuous  working,  66 
Rating  for  intermittent  working,  66,  67 
Reactance  voltage,  124-127 
Reactance  voltage,  limits  of,  129-131 
Reactance   voltage,    output  limited   by, 

128-131 
Reaction    voltage     of    armature.      Sec 

AKMATUBE  REACTION 
Re-entrancy,  definition,  89 
Re-entrancy,  101,  103,  109 
Resistance  of  armature.     See  ARMATURE 

WINDINGS 

Resistance,  commutation,  124-126 
Resistance  and  efficiency,   25,  28,   and 

Appendix  II. 

Retrogressive  windings,  94,  108 
Ring  windings,  90-93,  100 
Rockers,  166 
Ryan  winding,  121 


SEGMENTS  of  commutator,  164,  165 
Segments    of    commutator    covered    by 

brush,  135 

Self-induction,  coefficient  of,  122 
Self-induction,  calculation  of,  124 
Self-induction,  effect  of,  125 
Senstius  on  armature  heating,  82 
Senstius  on  armature  strength,  86 
Shafts,  formulEe  for,  156-158 
Shafts,  size  of,  156-158 
Slots,  dimensions,  15,  190,  205,  and  Ap- 
pendix I. 
Slots,   examples  of,   144,  145,  192,  206, 

217 

Slots,  effect  on  gap  density,  41 
Slots,  insulation  of,  144,  146,  190,  206 
Slots,  number  of,  15,  16,  115,  185,  204 
Slots,     space-factor     of.      See     SPACE- 
FACTOR 

Space-factor,  definition,  140 
Space-factor  of  armatures,  143,  147,  190, 

192,  200,  206 

Space-factor  of  field-coils,  141 
Speed,  peripheral,  of  armature,  24 
Speed,  peripheral,  of  commutator,  24 
Spiders,  use  of,  159 


240 


INDEX 


Spiders,  strength  of,  161 
Stalloy,  16-18 
Standardization,  33,  34 
Steel,  cast,  3,  4 


TEETH,  density  in,  15,  42 

Teeth,  number  of.     See  SLOTS 

Temperature-rise  of  armature,  Chap. 
VII. 

Temperature-rise  of  commutator,  86 

Temperature-rise  of  enclosed  motors,  65, 
87,88 

Temperature-rise,  examples  of,  76,  85, 
186,  187,  202,  208 

Temperature-rise  of  field-coils,  Chap.  VI. 

Temperature-rise,  final,  65 

Temperature-rise  in  armatures,  80-82 

Temperature-rise,  formulae  for,  in  field- 
coils,  70,  75 

Temperature-rise,  general,  63,  66 

Temperature-rise  for  intermittent  load- 
ing, 65 

Temperature-rise,  maximum  for  cover- 
ing, 69 

Temperature-rise,  measurement  of,  67, 
80 

Temperature-rise,  standards  of,  69,  70 

Thompson,  Prof.  S.  P.,  on  size  of  slot,  15 

Thompson,  Prof.  S.  P.,  on  temperature- 
rise,  71 

Traction  motor,  design  of,  213 

Two-circuit  windings.  See  ARMATURE 
WINDINGS 


VARIABLE  losses,  25 

Variable  losses,  ratio  to  constant  losses, 

30,31 

Varnishes,  138 

Ventilation  of  armatures,  161 
Ventilation  of  field-coils,  74,  75,  77,  150 
Verity's  brush-holders,  168 
Vulcanized  fibre,  137 


W 


WAVE- WINDINGS.  See  ARMATURE  WIND- 
INGS 

Wiener  on  temperature-rise,  71 

Windings  of  armatures.  See  ARMATUKE 
WINDINGS 

Wires,  table  of,  Appendix  VII. 

Wires,  coverings  for,  58,  139,  140 

Works  costs.     See  COSTS 

X 

X.     Sec  ELECTRIC  LOADING 
Y 

YOKE,  cost  of,  178,  179 
Yoke,  density  in,  13,  178 
Yoke,  examples,  178,  208,  218 

Z 

Zimmerman  on  temperature-rise,  79 


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ALTERNATING  CURRENTS: 

THEIR  THEORY,  GENERATION  &  TRANSFORMATION. 
By  ALFRED  HAY,  D.Sc.,  M.I.E.E. 


Demy  8vo.    178  Illustrations.    307  pages.    6s.  net ;  post  free,  6s. 

FOURTH  THOUSAND. 


CONTENTS.— Theory  of  Single-phase  and  Polyphase  Currents— Theory  of  the  Wattmeter- 
Measuring  Instruments — Alternators,  Transformers,  and  Induction  Motors — Synchronous  Motors 
and  Parallel  Running — Regulation  of  Alternators  and  Transformers — Testing  of  Alternators  and 
Transformers — Theory  of  Induction  Motors  and  Circle  Diagram — Testing  of  Induction  Motors — 
Induction  Generators  and  Speed  Control  of  Induction  Motors— Rotary  Converters— Compensated 
Induction  Motors  and  Compound  Alternators — Single-phase  Commutator  Motors. 

"The  best  book  ever  written  on  the  subject." — Electrical  Engineer. 


ELECTRIC  ARC  LAMPS:   THEIR  PRINCIPLES, 
CONSTRUCTION,  AND  WORKING. 

By  J.   ZEIDLER  and  J.  LUSTGARTEN,  M.Sc., 

Lecturer  in  Electrical  Engineering  at  the  Municipal  School  of  Technology,  Manchester. 


Demy  8vo.    Profusely  Illustrated.    53.  net ;  post  free,  5s.  4d. 

CONTENTS.— The  Electric  Arc — The  Principles  of  Arc  Lamps — Series,  Shunt, 
and  Differential  Arc  Lamps — The  Construction  of  Arc  Lamps — Open,  Enclosed, 
and  Flame  (including  Magazine)  Arc  Lamps — Candle-power,  Light  Distribution, 
and  Application  of  Arc  Lamps  for  Lighting  Purposes — Illumination — Accessories 
for  Installation — Tables — Curves — Appendix — Comparative  Cost  of  Different 
Sources  of  Light. 


THE  DISEASES  OF  ELECTRIC  MACHINERY: 

THEIR  SYMPTOMS,   CAUSES  AND    REMEDY. 

By  C.  KINZBRUNNER,  A.M.I.E.E. 
Limp  Cloth,    is.  6d.  net ;  post  free,  is.  8d.     Eighth  Thousand. 

Chapters  are  devoted  to  :  Sparking — Heating — Dynamo  fails  to  generate — Motor 
fails  to  start — Speed  of  Motor — Noise — Faults  with  Starters  and  Regulators — 
Alternating-current  Generators  with  Rotating  Armatures — Alternators  with  Rotating 
Field — Single  and  Multi-phase  Induction  Motors— The  Installation  and  Care  of 
Electric  Machines. 

LABORATORY  WORK  IN  ELECTRICAL 
ENGINEERING. 

By  JOHN  ROBERTS,  Junr., 

Of  the  Blackburn  Technical  School. 

Demy  8vo.     Profusely  Illustrated.    53.  net ;  post  free,  53.  4d. 

Laboratory  Experiments  for  First  and  Second  Year  Students  of  Electrical  Engineer- 
ing. The  work  contains,  besides  the  usual  pure  measurements,  special  chapters  on  the 
Potentiometer,  the  Calibration  of  Electrical  Measuring  Instruments,  Dynamo  and 
Motor  Tests,  &c. 

STARTERS  AND  REGULATORS 

FOR   ELECTRIC   MOTORS   AND   GENERATORS: 
THEORY,    CONSTRUCTION,   AND   CONNECTION. 

By  RUDOLF  KRAUSE. 

TRANSLATED  BY  C.  KINZBRUNNER  AND  N.  WEST. 
Demy  8vo.    Profusely  Illustrated.    43.  6d.  net ;  post  free,  43.  lod. 

Special  Chapters  are  devoted  to  :  Theory  of  Starters — Mechanical  Construction  of 
Starters — Calculation  of  Regulating  Resistances  for  Generators  and  Motors — Con- 
struction and  Connections  of  Regulators  for  Generators  and  Motors. 


ALTERNATING  CURRENT  WINDINGS;  THEIR 
THEORY  AND  CONSTRUCTION.  By  C.  KINZ- 
BRUNNER,  A.M. I.E. E.  Demy  8vo.  Profusely  Illustrated. 
35.  6d.  net ;  post  free,  33.  gd. 

"  With  diagrams  and  photographs,  the  author  has  succeeded  in  explaining  the  various  modes 
of  winding  large  alternators  more  clearly  than  words  alone  can  possibly  do." — Electrical  Times. 

TESTING  OF  ALTERNATING  CURRENT 
MACHINES;  GENERAL  TESTS;  TRANS- 
FORMERS; ALTERNATORS.  By  C.  KINZBRUNNER, 
A.M.I.E.E.  Demy  8vo.  Profusely  Illustrated.  43.  6d.  net; 
post  free,  45.  rod. 

For  both  Electrical  and  Mechanical  Engineers  who  are  engaged  in  test-room  work,  or  in 
installing  and  supervising  electrical  machinery  ;  also  most  helpful  in  preparing  the  student  for  his 
laboratory  work. 

CONTINUOUS  CURRENT  ARMATURES:  THEIR 
WINDINGS  AND  CONSTRUCTION.  By  C.  KINZ- 
BRUNNER, A.M.I.E.E.  Demy  8vo.  Profusely  Illustrated. 
33.  6d.  net ;  post  free,  35.  gd. 

Deals  in  a  clear  and  simple  manner  with  the  methods  of  winding  continuous  current  armatures. 
Suitable  for  students,  designers,  and  workmen. 

TESTING  OF  CONTINUOUS  CURRENT 
MACHINES  IN  LABORATORIES  AND  TEST 
ROOMS.  By  C.  KINZBRUNNER,  A.M.I.E.E.  Demy  8vo. 
Profusely  Illustrated.  6s.  net ;  post  free,  6s.  5d. 

Special  Chapters  are  devoted  to  :  Resistance  Measurement — Measure  of  Temperatures — 
Insulation  Measurements — Measurement  of  Speed — No-load  Characteristics — Load  Characteristics 
— Magnetic  Measurements — Efficiency — Separation  of  Losses — Practical  Testing  of  Continuous 
current  Machines. 

ELECTIC    TRACTION.  By    ROBERT    H.    SMITH,    Assoc. 

M.I.C.E.;    M.I.  Mech.  E. ;  M.I.E.E. ;    M.I.  and  St.  I. ;  Whit. 

Schol.      Demy   8vo.      465  pp.,   347    Illustrations.      95.   net; 
post  free,  93.  6d. 

"This  book  may  be  said  to  possess  a  unique  merit  in  being  a  handy  compilation  of  facts  derived 
from  practical  examples,  from  which  deductions  are  drawn  that  may  prove  valuable ;  .  .  .  one 
of  the  best  attempts  made  to  cover  the  field." — Times  Engineering  Supplement. 

ELECTRICITY  IN  MINING,  By  SIDNEY  F.  WALKER, 
M.I.E.E.,  M.I.Min.  E.,  &c.  Demy  8vo.  Profusely  Illustrated. 
95.  net ;  post  free,  93.  5d. 

"Among  the  apparatus  described  are  drilling  machines,  ventilation,  lighting,  mechanical 
stokers,  water  softeners,  economizers,  feed  water  heaters,  super-heat  condensers,  steam  turbines, 
internal  combustion  engines,  suction  plant  producer,  pumps,  haulage,  winding  gear,  locomotives, 
etc." — Ironmonger. 

STEAM  BOILERS,  ENGINES,  AND  TURBINES, 
AND  THEIR  ACCESSORIES.  By  SYDNEY  F.  WALKER, 
M.I.E.E.,  A.M.I.C.E.,  &c.  Demy  8vo.  Profusely  Illustrated. 
93.  net  j  post  free,  95.  $d. 

For  students,  and  for  those  engaged  in  the  use  or  manufacture  of  steam  boilers,  engines,  and 
turbines.  It  is  an  epitome  of  the  knowledge  and  practice  of  the  subject  up  to  date,  and  no  very 
advanced  mathematics  are  used. 

HARPER  &  BROTHERS,  45,  Albemarle  Street,  LONDON,  W. 


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Engineering 
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UNIVERSITY  OF  CALIFORNIA  LIBRARY 


